I've got no running lights on my trailer.

Brake lights and turn signals both work.

Where should I start looking for the problem?

Start with the light plug on the tow vehicle. Make sure you have all the functions on both sides of the plug. Then check the ground connection. My trailer made me nuts with intermittent lighting problems until I pulled new wire through the frame for all of the lights. I also ran a wire for all of the grounds instead of depending on sheet metal screws into the trailer frame.
Make sure you are getting ground through the plug and not depending on picking it up through the hitch ball.

Will do.

Thanks.

aint this a NEW Boat, if its not the truck, take it back to the dealer

It's a new boat. However the dealer is an hour and a half in away in each direction.

First thing to do is pull a lens off the lights and check the bulb/socket connection. If water got in they could be corroded. Happened to my Xpress trailer at less than 4months old. I replaced with LED fixtures.

After that, start at the plug on the truck, then work your back as suggested above.

They are LED lights.

Your Ground should be good or else none of your lights would work. I would check out the Brown wire as that is the one that runs your tail lights. It will be the #3 connection on a 7 pin harness, if a 4 pin its the one next to the ground. There is a chance also that you blew a fuse or relay. If its a late model Ford I would check.... I think its fuse #73 under the hood, its a common issue. Hope this helps.

It's a Dodge. I have a feeling it's a fuse. Later today when it's a bit cooler I'll go check the fuses.

look under the hood, fuse box, you will have 2 trailer fuses, one is blown.

Blown fuse.

It's some crazy size that no auto parts store carries. I'm going to have to go to a dealer to find a fuse.

its probably the new mini mini fuse, looks like the no probes extending down? they have them just dont know they have them

I hit three different stores yesterday. Two chain stores and one independent and they did not have them. They have the same type of fuse in the bigger size but not those mini minis.

You can still use a mini fuse, do it all the time at work