[JRTJH]

A couple of guesses (that's about all any of us can do from a distance):

Is it possible that water is running off the roof, onto the front cap (it's molded and looks like it would channel water to the lower front center) and then dripping onto the battery box?

Is it possible that the roof gutter that runs along the entire front side of the trailer is two pieces, where they join "should be sealed with silicone" and there is a gap or a bend that causes water to pool and drip onto the top of a slide?

And a suggestion:

Have you raised the front of the trailer a couple of inches to see if it changes the dripping sound? Lowered the front a couple of inches? Lifted one side or the other an inch or so? Any of those would alter the flow of water off the roof. Once you determine the low point, you may be able to follow the flow and identify a point where it's leaving the roof and dripping onto something below that area.