Thanks everyone for the comments. The seller is a good friend, and a very trustworthy person, but probably not the most mechanically inclined (hence why all maintenance was performed at a shop), and probably didn't notice a water leak if it started at the running light.
However, I am under no pressure to purchase the trailer. He totally understands if I decide to pass, as he acknowledges the potential for water damage. Since it's an aluminum frame, I'd assume my risk for heavy rot and such would be less than a wood-framed trailer?
The big issue here is my girlfriend/soon-to-be fiance grew up with a TT and camping has always been a big part of her life. Her dream is to own a TT, and this would be a very low-cost way of doing so. So if anyone is pressuring me to proceed, it's her. And obviously while I don't want to disappoint her, I don't want to set us up for failure down the road.