Update to the process: I ran a voltage test on the feed from the PWM with the truck brakes applied at varying levels. Max voltage to the trailer brakes was 4.2v. Even with a capacitor in the circuit leading to the relay, would that be near enough root voltage to activate the relay?Well, it does sound like something may be wrong with the meter.
If the LED didn't light then you had no continuity through the meter.
Perhaps it's fused and the fuse blew.
Also, it has occurred to me that this travel trailer has an onboard 12v battery (as most do), so a source of constant and steady 12v power for the new 3rd LED brake light is right there onboard.