You didn't say what model fun finder it is. I have a 2008 Fun Finder X 189FBR. I can help you if your model is similar. Is it fiberglass or aluminum sided? If it's fiberglass (smooth sided) the ceiling is thin plywood laminated over about 2-3" of styrofoam. Good news is I think it really can't rot, although I suppose I could be wrong.
The caulk I recommend is Proflex RV sealant - it's great! Soapy water will smooth it. You can put it on when it is raining (that's when I've found leaks LOL) https://amzn.to/2TUWHfx
It comes in white, clear or some colors.