The service manual shows that the tire pressure monitoring control module should be located behind the trim in the left side cargo compartment:

However, it's not present at this location in my Mini:

Does anyone know where I can find the tire pressure control module/RDC in my R56?

 

This thread says that, for a R56 lci, the RDC control module is located behind a foam insert in the rear bumper. I'll look for it there tomorrow morning.

 

While looking up from below the passenger side of my rear bumper, I could not access the area of bumper foam shown in the thread linked in previous post due to the muffler exhaust heat shield. However, behind the passenger side trim in the cargo compartment, I discovered a wire bundle that was routed behind the rear bumper cover. A pair of twisted K-CAN wires (green and orange/green) in this wire bundle suggested that the TPMS/RDC control module would be found behind the rear bumper cover.

 

I found the TPMS/RDC control module (red rectangle) tucked into the foam pad behind rear bumper cover on the driver's side.



Same location as reported in this thread.
Zoomed in view:



Removed and cleaned RDC module:




The module has 4 male pins, with pins 1 & 3 connecting to two K-CAN lines and pins 2 and 4 connecting to battery voltage and ground. (Same as module connector pinout posted in this thread)



In my 2012 Mini:
1) When RDC module is connected, my code reader shows an active code D904 (CAS: K-CAN wire fault).

2) When RDC module is disconnected, my code reader shows an archived, inactive code D904 (CAS: K-CAN wire fault) and an active code A3C3 (Instrument cluster: Tyre pressure control, communication fault).

3) When RDC module is reconnected, my code reader shows an active code D904 (CAS: K-CAN wire fault) and an archived, inactive code A3C3.

 

Problem solved.

K-CAN fault code D904 was caused by the nearby K-CAN wires that run to the RDC module connector. The green K-CAN wire was severed and the orange/green K-CAN wire had damaged insulation and an underlying corroded wire. The damaged segments of the wires were removed, and the wires were soldered back together. The Mini is now fault code free!