Grassroots trailer roof repair

This is for another type of "horsepower", but since many of you have trailers and campers and such, I thought this would be the best place to ask.

The roof over the tack room on my wife's horse trailer leaks terribly when it rains, (making all her tack and armor quite moldy) and here we can see why. It's like this in several places around the perimeter where these corner plates attach.

What kind of sealer do I need to fix this? Is there something that brushes on, or do I scrape as much old goo out as I can and inject some sorta caulk in there?

I used this tape for the seam around the roof vent in my van and was very impressed with the quality. It is a thick adhesive with a stretchy vinyl-type backing that conforms to screw heads and seams easily. 

COFAIR PRODUCTS UBW425 4x25 WHT Ultra Bond - Automotive Adhesives And Sealants - Amazon.com

I would probably use Dicor lap sealant. It's designed for RV and trailer roofs. It's what I used on SanFord and it has held up very well. 

It comes in self-leveling for flat surfaces and non-sag for vertical surfaces. 

For cheap and dirty, Flex Seal tape works. But it's ugly. Toy man!'s suggestion is good stuff... I have not seen or used the other tape mentioned. I'll have to check it out. 

Dicor lasts about 5-6 years here in S FL in full sun. Need to redo my trailer again.

Belt and suspenders. Clean it really well, put down the calk that really really sticks, and then covert it with eternabond tape. 

I've used something similar to what Evan posted, but it's called Eternabond tape.  It claims to be a forever thing and it's held up really well for me for several years.  Goes on pretty easily, will encapsulate any silicone that someone may have smeared on there, and winds up looking pretty nice as long as you apply it in a straight line.

A lot of the Airstream and similar folk like Eternabond.  Requires a roller to really push it down to seal.

Recommended to scrape all the initial stuff up, clean with acetone or M.E.K., scuff with a scotchbrite pad, reclean with solvents, apply when dry.

In reply to Mr_Asa :

I have successfully applied Eternabond by lightly blowing (most of) the loose stuff off, slapping the tape down, and pushing on it with my palm.  Your way is probably the right one, but even when applied wrong, the stuff still seals like a mofo.

Thanks for all the suggestions. I think I'll fill the obvious gaps with the Dicor, and put a strip of Eternabond on top to hopefully ward off future problems.  To the RV store I go!