Where’s a good place to start looking for a short? The port side tail light works but no turn signal or brake light. When the standard halogen lights were in, the brake light would gradually come on. There’s new LED lights in there now and just the running lights work. The starboard side works great as it should.
Any thoughts?
When a lamp doesn't illuminate, for some reason people immediately think "short circuit". If you blow fuse after fuse in the tow vehicle, you have a short circuit. If you do NOT blow fuses in the tow vehicle, it is extremely unlikely that you have a short circuit.
The most common problem with lamps not energizing is an OPEN CIRCUIT. This means that a conductor isn't making contact. Either the positive conductor or Ground conductor could be disconnected at some point along the circuit; either one or both gives the same no-workie result.
Trailer lamps at a given lamp fixture share one common Ground. Since your tail light works, that tells us the Ground is making contact at the lamp housing, so the Ground connection isn't the issue. This narrows it down to a single wire - the positive conductor for the brake & turn function. [Note that the same LED or filament provides both brake and turn functions.]
Turn/Brake on the left lamp housing is energized by a yellow wire if the trailer is wired correctly.
Turn/Brake on the right lamp housing is energized by a green wire if the trailer is wired correctly.
Your issue is with the yellow wire - or some connection for that wire. Corrosion in pluggable connectors or other wire splices, or a faulty connector installation (butt splice) are the typical culprits. Occasionally, the wire itself may be found to be physically broken due to an encounter with road debris or getting snagged on something when the trailer moved.
You seem to not have an issue on the right side, so swap the two fixtures (temporarily just for a plug-in test). If the issue is the trailer, the left side will still have a problem when you plug the other fixture in. If the problem moves to the right side, then the issue is with the lamp assembly you had installed on the left side.
When you unplug the connectors, inspect them for corrosion or heavy tarnish. They may need to be cleaned up with a soft metal bristle brush or fine grit emery cloth (not typical sandpaper - way too coarse). Also trace the yellow wire to see if it is damaged along the path to the trailer tongue. Realize that a disconnect in the yellow wire could be all the way at the trailer tongue as well. The splice that attaches the tow harness connector could have an open circuit. A digital voltmeter or test lamp is useful for diagnosis of problems such as this. Problem isolation should take mere minutes with this info if you have a test light or DVM. You'll need to connect the tow vehicle and turn on the left turn signal to chase down the open circuit using the tools. I can judge most by sight, and fix the obvious without bothering with more effort if my guess fixes it....