Hi, SCRFT0001! I also have an '86 Class C and I recently worked on my roof. I used a putty knife and removed the old caulking and then cleaned up the seams and all things sticking through the roof (vents, etc.). Replaced with an elastomeric caulking (like dicor). Wash the roof with TSP which helps with all the black streaks running down the sides. I plan on applying Snow Coat on the entire roof but I have other concerns right now that require my attention.
What I found when redoing the caulking, was that it is very important to take your time and do it right the first time. I thought that's what I had done until the first rain! I ended up with a leak and when I tracked it down I found a small spot that I had missed when up on the roof. I caught it while on a ladder and looking at the seams. Just a tiny area, but enough to cause the leak. We've had rain since, and not a drop inside now (from the roof anyway)!
I still have a window (over the cab) that needs a new frame around it. It seems to have "shrunk". Anyway, I will still get some water from that.
Do read Fleamarketer's "my roof repair". If it doesn't scare you, it's well worth the read! Everyone is really great here and helpful, so post often about your concerns. Good luck.