If the tow vehicle was built after '06 (Manufacturing quality of all brands took a nosedive for '07, especially with GM), check the vehicle for power first. If that checks out, concentrate on the trailer.
If you've got power at the sockets, then the bulbs are bad, or you've got extremely chinese lamp assemblies. I've seen corroded sockets prevent a good ground, and I've also seen dual-filament bulbs short across the brake/tail to running lamp circuits via a blown filament. I've seen chinese assemblies that had bad grounds internally, and poor contact due to loose and extremely cheap sockets. I've also seen bulbs that visually looked 100%, but had an open circuit somewhere inside the light that was NOT the filament.
Short circuits are extremely common in all wiring, especially when trailer manufacturers run wiring through washers welded to the frame (Dively) with zero protection for the wire.
In the Northeast and anywhere else road salt is used through the winter, corrosion of literally EVERYTHING is an issue, especially connectors, plugs, sockets, or any break in the wiring insulation.
Voltage drop testing is your friend. Plenty of YouTube vids on the subject. Anything more than 1/4 (.25) volt can cause issues. On LED lights, I'd want to see no more than 0.10v drop. A volt or more is definitely causing issues. If your meter reads 12v, that means there's a 12v drop ... AKA, ZERO volts. Good luck!