go to this page---https://www.easternmarine.com/em_store/lighting/
scroll down so you can see the wiring color codes/what wire/plug location does what. Then start checking continuity. You can put the meter on the vehicle ground (somewhere--not painted metal) and on the trailer (not painted) when the lights are plugged in and you should get near zero resistance (ohms). if you don't then you have a ground issue between car and trailer--and they have to be one and the same potential-- since the car battery is powering the lights on the trailer.
Make sure that is resolved before you do anything else. Once you have a good ground- between the trailer- and the car or truck- you can start isolating each individual light circuit- but it sounds like once you get your ground straight this will solve most of your problems.
Once you know you have good ground, check for 12v. Put the parking lights on and make sure the 12 v is coming thru ---even if the lights dont work- just make sure you have 12v. If not- then its shorted or ---once again- there is a fuse or wiring problem to the connection between trailer/truck. Once you get SOME light working- then its much easier to sort out the problem and get the right colored wire to the right light. You don't know if your lights are all good, fuses all good, ground, or connections--so start with most likely (ground) and work thru the list.
This is not complicated---frustrating at times yes- but not complicated. Don't over complicate it. Just think about it and study the diagrams on the website I sent you too--that is the standard for all boat trailers so once you get it right- your truck will properly light any boat trailer.
The ground has to be first or nothing will work. Then- the powerIf you need help, we are here. I am new to this forum, but I am an electrical engineer and it sounds like the other guys are equally as or much more knowledgeable than me- so there is plenty of help.