Found my leak - should I try to dry out the area?

You're in Florida right? so it's relatively warm. I would make sure the
camper is exposed to the sun to warm it up and then run the heater/furnace
to warm up the inside. This may help evaporate any water;

A dehumidifier will help keep the air dry

An electric dehumidifier will go a long ways toward drying the interior of the camper.

I first noticed the water in the light fixture above the bathroom sink. The area around the hole seemed dry. There was also water on the floor under the area where the roof membrane was cut, so some water made its way down the wall as well as across the ceiling. I could cut a hole in the area behind the lower cabinet to take a look and to vent the area inside the wall. Thanks for the suggestion about the speaker hole. I may drop a speaker and look through there. There is also a large access hole to the "attic" through the vent on the roof for the refrigerator.

I don't know where your leak showed up inside your TT but, on mine I was able to remove a speaker from the ceiling and blow air up there with a fan until it was dry. But, I only had a small leak in one area and the water was dripping out of the speaker before I removed it

I

It would have been best to dry the area before applying the Eternabond.
But, I would still try to dry it as best as possible without removing the E/bond.

My question would be what caused the leak for the roof membrane to be cut so cleanly. If it is a problem that membrane is to short, then entire trim strip portably needs to removed. Dry out the area below, them put Eternbond along edge and put trim back.
Any time you have a leak, the water needs to be removed, as it will continue to cause deterioration and rot in wood. Also water could have gotten into the wall too.