Welcome to the forums and, yes, this web site is very active. I think a good portion of us live here! It's more entertaining (and sometimes informative) than television. You'll get all kinds of answers, some you'll agree with, some you'll disagree with.
About your camper. If it were mine, considering it's age and the fact it was a FEMA camper, I'd not worry too much about cleaning the old calking off the roof. I'd just go over the old and make sure the new covers the cracks very, very well. If you begin to dig too deep on the roof, you may end up having to do much more work than you want. If there is some roof rot because of the leak, you may be able to get away with it, providing the wood is now dried out and still has some good strength (not too saggy if you put weight on it).
It would be best to use Dicor Lap Sealant. Most RV dealerships sell it. The problem with different sealers is the danger of their chemicals deteriorating your rubber roof, making it even worse.
If it were a newer camper, I'd consider a different path. But for an immediate and quick fix, this is what I'd do until I got to know the camper better. It's just too easy to get in too deep with water damage that may end up being way more work and expense than you thought. Start simple. If it does not work, then go to the next level.
Congrats on your trailer purchase and welcome to the forums!