01M Shifting Issue in 2001 TDI

I have a 2001 TDI that doesn't shift out of 1st. Transmission itself doesn't appear to have any problems, I suspect the issue is related to the multifunction switch and/or the TCM.

Symptoms are:

1. Gear selection doesn't work. Selecting P,N and D on the shifter all leave P displayed. 3,2 and 1 illuminate nothing or 1 on the display.

2. Transmission doesn't shift out of 1st gear when in drive. Park, Neutral, and Reverse all function fine.

3. VAG com shows that one digit from the binary gear selection code from the multifunction switch doesn't change from 0. I don't recall what the codes are supposed to be precisely but for example

P should be 0001 and actual is 0001
N should be 1001 and actual is 0001
D should be 1010 and actual is 0010
3 should be 1011 and actual is 0011
2 should be 1100 and actual is 0100
1 should be 1101 and actual is 0101

Shift lock solenoid functions fine.

This results in the TCM not knowing which gear is actually selected and I suspect the shifting issue.

My question is... how do I confirm this diagnosis without purchasing a new TCM?

I have confirmed that all the wires in the harness have continuity from the multifunction switch to the TCM and no apparent shorts. Multifunction switch appears to function properly but could be faulty. Unfortunately replacements are expensive. TCM's are also expensive. Has to be one of the two unless I'm missing something.

There are no transmission codes or engine codes. Wheel speed sensors are throwing codes but I doubt they're causing any issues other than switching on the ABS light

01M Shifting Issue in 2001 TDI