Good luck on your brevet attempt! The answer has been modified a bit from the original. I'm assuming that the OP's going to be riding for at least 7-8 hours, not including breaks.
Note: I initially recommended that the OP drink ahead of thirst. In comments, @whatisname contended that this advice is based on a myth. On further research, I modified it.
The quick summary is that thirst perception is a good guide. If you're riding in very hot conditions, it may be worth it to drink ahead of thirst, and you also want to manage your electrolyte consumption. You do not need to replace weight lost 1 for 1. With time, riders will develop an intuitive sense of their water and electrolyte needs over time. if you're craving salt during or after a ride, then you can add more salt to your drinks.
Thirst perception
Just drinking to thirst is sufficient most of the time, but also consider electrolyte intake (described further below).
The OP may not exactly be in a normal situation. This is a very long ride, and it may be hot. If true, it may be worth drinking ahead of thirst. This issue may be more prominent later in the ride. This is based on personal experience, not anything empirical. Our thirst perception declines with age, so athletes over about age 65 should err on the side of drinking more as well.
Individual fluid consumption varies a lot. You probably develop a sense of your needs over time. One can obviously start from a rule of thumb, e.g. one bottle per hour as proposed by @DavidW, and adjust based on your perception of thirst.
For example, I drink a lot more than my ride buddies. Some of them start a weekend with just one bottle, even in the heat, but I always carry two full sized ones. In temperatures of 85F/30C and higher, I find that I can easily drink a 25oz/750ml bottle per hour. By two hours, my less thirsty friends have finished their lone bottle.
Drinking ahead of thirst isn't necessary
British Cycling recommended that cyclists drink ahead of thirst, rather than just to thirst. They argued that thirst is a lagging indicator of your hydration status; when you feel thirsty, you are in a significant deficit. However, Allen Lim, who has worked extensively with professional road cyclists, countered on a podcast that these athletes were good at listening to their perception of thirst. He felt that perceived thirst was enough for them, and that they would generally hydrate themselves enough based on drinking to thirst. That said, these are professional athletes, and they train very extensively, so their perceptions of their bodies are well-developed.
Andy Blow, an exercise scientist writing for the TrainerRoad blog, argued that thirst alone is a good general guide in most exercise conditions. He argues that heat and exercise duration may modify this. I based my argument above on his post.
If you want to measure your fluid intake
It's not strictly necessary, I think, but you can measure your fluid intake like the OP outlined. That is, weigh yourself before and after the ride. But you need to account for your fluid and food intake if you do this. Not accounting for food, you have 1) the difference in your start and finish weight, and 2) the amount of fluid consumed. The total is the amount of fluid lost. Divide that by time, and you have an estimate of sweat rate.
You don't need to replace all the lost weight
Precision Hydration (NB: they sell hydration products) points out that in a very long event, the amount of fuel you burn (and expel as CO2) can start to confound the measurement. For example, at zone 2, I can burn around 400 calories (estimated, probably at least a 10% margin of error in either direction) per hour. If it were half carbs and half fat, that's 50g carbs and 22g fat (NB: you can't practically measure your carb:fat oxidation ratio on a ride, so I assumed). For a 2h ride, I'd ignore the difference. But for a 5h ride, that's 375g, a bit over 0.8lb. A relevant abstract describes some other mechanisms the weight difference can be confounded.
In this blog post, Precision Hydration reviews some case studies. Since 2007, the American College of Sports Medicine issued a guideline to keep water loss under 2% of body weight. However, a lot of elite Ironman or marathon athletes lost 1-6% of bodyweight during their events.
Clearly, it's possible for at least some people to tolerate over a 2% bodyweight loss. It seems likely to me that you may need conditioning for this, and there's almost certainly individual variation in how much loss is tolerable.
The pre-2007 ACSM guideline was full replacement. This, plus the fact people didn't consider sodium levels, may have led some athletes in long and hot events to develop hyponatremia, i.e. sodium levels too low, caused by dilution.
The role of electrolytes, particularly sodium
The OP clearly recognized the need for electrolytes, but I felt that more info would help others.
When I started cycling, I'd drink plain water, only to find that I'd crash at the end of long rides in the heat. This changed considerably when I started using electrolyte drinks. The rate at which we excrete sodium is highly variable - Precision Hydration says they have seen some athletes who lose 200mg Na/liter of sweat, and some who lose 2,300mg or more. Everyone's drinks should contain some sodium.
You can develop a sense for how much salt you need to take in over time. After rides, do you crave salty food? That means you need more. Also, if you have very salty sweat, you will see significant salt deposits on your exercise gear after a long workout, or dogs may lick you after a workout. Your sweat stinging your eyes is another indicator. Personally, I get some salt deposits in some circumstances, but not a lot. I infer that I'm probably near the average in terms of salt concentration, although my sweat volume is very high.
On my last 5h endurance ride at about 90 degrees F, I took about 1000mg sodium plus 250mg potassium in a drink, plus I dissolved a bit of salt in some maple syrup. This seemed sufficient, and I didn't have an unusual craving for salt afterward. I might experiment with higher salt content in the future.
If you know nothing about your own sodium needs, maybe start with a pre-mixed drink that's got about 400mg sodium. Aim to do a bottle of that every few hours. Titrate your intake from there. It probably isn't necessary to replace potassium, even though the mix I bought had it. You can actually just use table salt, as I discussed here. 1 teaspoon table salt has about 2,320mg sodium. I add this to my flask of maple syrup, or you can add it to a non-electrolyte drink, or you can make sure you eat food with salt (e.g. jerky).
This ties into the role of carbohydrates in sports drinks
Carbohydrate in your drink may affect how well you absorb the fluid, but you do not want your drinks too sweet. Lim argued that a drink that is too concentrated (i.e. has too much sugar and other material dissolved) actually inhibited how well athletes could absorb the water content. Basically, the sports drinks had a higher concentration than our blood, and due to chemistry, this tends to pull water into your digestive tract rather than into your blood. Lim reported that many of his athletes developed bloating or other gastric distress from too-concentrated drinks. While you need to replenish carbohydrate stores while riding, I would not rely on sports drinks to do this.
Lim runs a company called Skratch Labs, and their drink mix contains about 20g of carbs (i.e. 80 calories) in a 16oz / 500ml drink, plus 400mg sodium and a bit of other electrolytes. I'm unable to find consistent nutrition information for Gatorade on the web, but I believe this is half or less the amount in an equivalent Gatorade serving.
Specialist cycling hydration mixes are available, but they can be pricey, and you can brew your own. The section at the end of the answer has some suggestions.
How much fuel?
While the OP didn't ask, the discussion about carbs does naturally tie into the role of fueling during exercise. Also, sodium with carbs does increase the drink's absorption rate. Cycling for very long distances burns a huge number of calories, and even Gatorade alone wouldn't be able to replenish them adequately. For example, my power meter estimates that I burn about 400-500 calories per hour at Z2-ish pace. I'm relatively small, and a larger rider probably burns more than this.
Your body stores carbohydrates in the form of glycogen. You will deplete your glycogen stores after about 3 hours of cycling. This will cause a bonk, which is very unpleasant.
You obviously don't need to replenish all the carbs (and fat) you burn. Lim proposed that athletes could aim to eat about half the calories they actually burned per hour. And as far as I know, riders on a diet should still have simple carbs when doing a long ride. The metabolic consequences of ingesting a lot of sugar don't apply because you aren't ingesting excess sugar.
Pre-made ride food has advanced a lot. But the modern stuff can be expensive, and is probably not necessary for a lot of people. Fresh fruit, if available, contains water as well as carbohydrates, and it can make for a good healthy snack at rest stops (but note that too much fiber on a long ride can upset your stomach, so experiment to see if you can tolerate this). Confections like chocolate bars, cookies, gummies, and candy bars will also work, although note that their fat content may also cause gastric upset (so experiment). Or there's your favorite full-calorie soft drink. A lot of people straight up get sick of eating later in the ride, so you may need to put some effort into feeding yourself. Seek variety if you need it.
One of my weaknesses is that when I'm solo, sometimes my planned stop doesn't have anything I regard as palatable, so I skip eating there. This happened last week. Then I'm underfueled in the last hour or two. More egregiously, there's a Burger King about 1.5 hours away from home on one of my routes. I thought the fat from the french fries would slow digestion, but in fact I could have got a small order of fries. Or if not that, I should have stashed an extra gel in my handlebar bag. Try not to fall into traps like this.
Notwithstanding what I said above about gels and the like, they're convenient and palatable. The mix I took lets you carry 60g of carbs in one bottle, possibly more. That said, you can actually DIY this using table sugar and table salt.
Drinking ahead of thirst not actually necessary
This answer initially advised to drink ahead of your thirst. This is actually a myth.
Tim Noakes, interviewed in Outside magazine, is an exercise scientist who advised on the dangers of over-hydrating during long endurance events. Indeed, if you take in too much water without also taking in sodium, your blood sodium levels can drop too low (i.e. hyponatremia). This can be dangerous. In fact, a number of marathoners have died from hyponatremia.
Blow, on the TrainerRoad blog cited earlier, responded that Noakes may be exaggerating the evidence. Blow countered that there is significant evidence that many successful athletes take on supplemental sodium during exercise. Blow did agree that drinking plain water (i.e. no electrolytes added) was generally sufficient, emphasis mine:
And for many people training or racing shorter events in cool to moderate conditions, drinking water to thirst will be sufficient most of the time.
He also added that we have some room for error; if you under-hydrate on a two hour ride, you can push through and just drink more afterward.
However, he cautioned that if you're in a long event on a hot day, that's not really a normal situation. You may also have trained hard up to that event, and thus depleted your existing reserves. In this case, drinking plain water alone to thirst is not likely to be sufficient. Thus the extra advice.
For those of us who need low sodium intake due to blood pressure, I would advise consulting your physician.