Did the person who wired your vehicle plug do so with the trailer attached to your vehicle?
What you really need is for the person who wired the seven wire RV plug to make sure everything is correct.
There is a standardized color code for trailer wiring but because we do not know if yours is wired to standard, discussing wire colors here will not help you.
It might be possible to wire a hot lead to the trailer's battery but there is a good chance that if you do a lot of stop and go driving the battery likely won't charge fully.
Like I said, most people that I see with these trailers use a battery charger built onto the trailer and plug it in nightly to charge.
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Click image:
[Image courtesy of etrailer.com]