Unlike the walls in a house, the RV walls move quite a lot and most any caulk will not hold long. It's only an appearance item at best, so better to leave it looking unfinished if we are not used to the idea than to have a crack in the caulk which looks worse?
For what leaks in the area between a shower and stool? There are lots of potential leakers, so it will need some study to sort which? It's a good move to have noted that is seems to not be fresh water leaks due to the pump not doing a cycle.
If we move the thought over to saying it is a drain or other than the normal fresh water leaks, it still leaves quite number to check.
One obvious would be the seal around the shower door as it can run to spots away from the real leak and come out at a different spot before we notice.
Water from the shower can get in behind the faucet, run down and follow the joint between pan and walls in ways that make it show a long distance away from the real problem at the faucet! Tricky part on that is it may not act like a leak when showering but come out after a bit of time!
A leak at the base of the stool where there should be a wax ring or other seal can be fairly common , depending on what it was done if the stool has been taken out and put back. Lots of folks try to reuse the old seal and take a chance!
Then there are often "air admittance" valves hidden in the wall and they may hang up to let water leak out and be very slow to show as it can be just a tiny bit at a time. Or there are times when this valve gets loose from it's attachment and turns over to create a leak.
A crack in some part of the stool?
Depending on how you use the RV, I might start with checking the shower as a source?
Possibly pull the shower faucet to look/feel behind it for any signs of leaks there? Water getting in for some time will often leave some sign things have been getting wet. Maybe a different way would be to make sure there is a good seal behind that faucet as a way to rule that out?
A tough one to sort but we have to start at some point and remove the questions in some fashion or order!