[Sammy Sandbag]

The tail lamps are controlled by trailer tow relay 1 (located in the Fuse and Relay Box.) Power is supplied to the tail lamp relay and a 10A fuse. The fuses and relay are located in the IPDM E/R (intelligent power distribution module engine room) which is just behind the relay box with the tow relays (next to the firewall.) The fuse is No. 36.

I would think you'd lose both tail lights if it were a fuse, since they follow the same circuit (in regards to just the tail lamps.) Now if it's just the turn signal and hazard (have you checked the hazards) then that it is controlled by the BCM and is seperate for left and right. Left is through BCM terminal 52, and power is supplied to trailer connector terminal 1 (your plug should have a schematic.) There is no fuse between the BCM and trailer, so nothing really you can check. BTW, the wire should be Green with a Black stripe.

Brake lamp power is supplied through a seperate terminal, based off of tge actual pedal.

So it's a bit confusing that both your left turn signal and brake light are not working. I could maybe see just the signal not working, but the left brake should work if the right does. Have you checked this with the running lights off (headlights completely off?)

Also, had you checked your lights following the BCM TSB? All this info is based on the '05 Titan prior to the fix, I have no idea what they might have done since then. Perhaps they messed up something during the fix.