Kickstands historically mount to the underside of both chainstays, just aft of the bottom bracket. Many bike frames incorporate a stiffener plate here, with a large bolthole for a stand. You do not need this stiffener plate for a stand. Example:
This stand clearly clamps an upper and lower plate around the chainstays and you can see the stiffener aft of that, as a tube on this frame.
However there are many other options:
Not quite a kickstand, but there are items intended for tourers where the traditional kickstand might be unreachable or obscured. Its essentially a long stick, often collapsible, that props between the ground and your saddle, or some other high point on your bike.
A tourer is weight-conscious, so these can substitute for a tent pole to get double duty out of the weight. You could use any lightweight stick wedged under the saddle too, doesn't need to be fancy.
There are stands designed to work off the front wheel, but they still require a second stand elsewhere. The front wheel kickstand cannot hold the whole bike.
A third option is to use a rear propstand, instead of a kickstand. This clamps to the rear axle on both sides, and stands the whole bike up.
These are more common on heavy bikes like cargo bikes or dutch utility bikes, they are relatively heavy, all on the rear axle, and probably will not work with disk brakes.
As per your answer, there are clamp-on stands for the left chainstay that may extend up to the seat stay for additional security against rotation.
Some kickstands secure under the left-side rear axle nut and point rearward when stowed.
Finally we should consider the null-case of no-stand. The world is full of things on which one may lean a bicycle. Bike rack/stand, trees, fences, bus stop/shelter, poles/traffic lights, etc
You can also lay your bike down gently on almost any surface without causing damage, though they do take up more space this way.
If you're riding with someone else, each bike can lean against the other. This takes some care but is totally possible.