You'll probably want DICOR lap sealant, comes in regular and self-leveling. The regular stays where you put it. The self-leveling is a bit "runny" and spreads out evenly (sort of) before setting up. Both are easy to use in a caulking gun, fairly cheap and available at any RV supply outlet. The chemistry is made to work with your rubber roof.
If this is a used trailer I'd get 3 -4 tubes and take a "shotgun" approach. Also look for cracks in skylight bubbles, plumbing vents, that sort of thing.
Inspect the seams along the end-caps and look for tears in the roof membrane.
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