I'm about 3500 miles into a long tour, and the other day we noticed a few of the wheels between my own bike and some other guy's were starting to warp pretty noticable. With the help of someone more versed in maintenance we tightened some spokes to true them against the brake pads and gave them all 1/8 turn on the advice they were a little loose. Another few days riding revealed in the course of this fix we warped the rim a little from circular (radially untrue?) so I did my best fixing that a little. My only worry is in somehow making the bike unsafe to ride since I'm new to truing wheels. On the road and without a means of measuring spoke tension, does it seem excessively risky to eyeball the tensions like this? My main worry, reasonable or (hopefully) not, is I'm somehow crippling the wheel and it will give out catastrophically at high speed or something. Is this fear founded at all? I'm curious how the wheel would fail if I'd messed it up.
Unfortunately there's not many aspects to truing wheels this question doesn't touch. Also unfortunately, figuring out what's going on with a given heavily used wheel with issues and then making it as good as possible are both beyond-the-basics wheel work skills.
Yes, it's possible to set yourself up for a bad situation here. The main ways you would do that are by allowing some spokes to be too loose (making them prone to go all the way slack, which both allows the nipples to unscrew and makes the wheel less strong/stable), having them all too loose (making the whole thing weak and prone to going out of true), or having some or all of them too tight, which can cause fatigue cracking.
It is critically important you understand and are able to spot the difference between truing a rim that's in good condition (would be flat and round if it were a bare rim with no forces acting on it) and truing a damaged rim (would be not perfectly round or flat instead). In the former case you're equalizing spoke tension on each side to make the wheel true. In the latter case you're creating intentional tension disparities to make the wheel look true and limp along having a greater or lesser degree of the above mentioned issues with too-tight or too-loose spots, and it usually won't stay true under touring conditions if there's very much of this going on at all. (Although conversely, wheels can handle some amount of this without incident.) Making this distinction empirically is one of the few things tensiometers are reallly good for. Doing it without one is fine too, but generally takes some experience to be confident about.
It's worth noting here that it's common for even rims in good condition to force you to have a little bit of tension disparity and/or out-of-round at the seam.
It's also worth noting that in the case of a rim with some radial damage only (flat but not very round), if you must keep going with that wheel, it can be reasonable to make the spoke tensions equal on each side and just accept it's not going to be very round, which you'll probably feel while riding and will require rim brakes to either be backed off or adjusted around the warbling tire, and never let the pads touch the tire. There are a lot of wheels running around the world with minor versions of this problem.
Wheels that are sufficiently overtensioned and/or unevenly tensioned can in fact give out under high speeds or from side loads, and a loaded up touring bike is a very probably venue for this to happen.
For a normal wheel with 32 or more spokes and a metal rim, I'd say you are pretty safe. Even if one or two spokes ended up breaking, there is enough redundancy to avoid catastrophic failure. Myself I'd probably continue riding even if one spoke broke.
However, if you have one of those super-light 16 spoke wheels or a carbon fiber rim, be more careful as they have been optimized for the minimum necessary strength and have less margin for unbalanced tension.
To roughly balance the tension, you can pluck the spokes after adjustments and listen to the sound. You can hear if a spoke is very loose (low sound) or very tight (high-pitched sound).