Hi, I have been troubleshooting my 2001 Audi A6 turn signal issue, and not sure where to go from here.

The front Right signal does not blink when turn signal is on, and when the hazards are on. The bulb works itself, because it turns on when my parking lights are on. I tried cleaning the hazard relay and that didn't fix it, so I ordered a new relay. Tried the new relay and it still doesn't work, so not sure where to go from here...
When I activate the right turn signal, I get rapid clicking, and my rear right flashes really fast.

 

I heard it could be a turn signal stalk issue. But I wonder if theres a way to troubleshoot before I buy this 50 dollar part.

 

I have not pulled one of these bulbs, but they should be dual filament: one for parking and one for turn. It is possible the former is fine but the turn signal filament is broken. The cheapest test is to replace the bulb with a new one or use the bulb from the left side, as you know it works. The fast clicking sounds like a failed bulb.