That sounds about right, F5 has a good point on your test battery connect the NEG to ground on the camper, then use your test light to ground on the camper. this ensures all the grounds are OK, and if it's gonna take you longer than me a heavier battery might be better. I used a small one back then because I didn't trust the camper wiring and didn't want to get bit hard
For the brake controller not sure how to "test" that without a lot of wire between controller and trailer but since you have a new vehicle it's a safe bet the wiring is correct on the truck side. I'd make sure everything else is wired right then plug it in and make sure your controller "sees" your camper.