Turn your lights on & Using a test light hooked up to a good ground (chassis or battery), check the white & purple wire pin in right tail light connector. Lights up = good power. Hook up test light to battery positive & check the black wire pin. Lights up = good ground. If it lights up both times, then wiring & module are good, likely need a new light socket. No test light on white/purple indicates either wiring problem or bad module (underhood fuse box for yours). No test light on black wire indicates bad ground connection or wire issue. Like hoot said, check front lights. If right front works, then the module should be good as they share the same power output & you would then need to start looking between tipm connector & ground.
Chasing wiring sucks. Eliminating easy parts of the circuit can save lots of time & hair pulling.
EDIT: also check wiring continuity with volt meter. With key & lights off, check the black wire terminal from tail light connector to chassis or battery ground. Also check the white / purple wire out of tipm c7 connector pin #6 (there's about 8 connectors there, donno off hand which one exactly) to tail light. Most diag flow charts say anything under 5 ohm's is a good wire.