If you do not have oscilloscope you could try connecting small high impedance speaker like from old phone, it's quite low data rate bus so I think if there is any data going you should here some noise.

Did you ever fix this. My fan is erratic as well, I was thinking it's the fan itself and I do have a new fan ready to go in. I was going to do it today but looking at the work involved I was thinking if I should get the regulator on standby as well just in case. Don't fancy taking it all apart in this cold just to find out that it's not the fan as I found out that even when fan is working measuring blocks still show 0.000A

I noticed that mine was more likely to work when doing left turn and more likely to not work when doing right turn. So it seemed like classic brush/commutator wear problem. As a result I attacked it without spare control module on standby and it was faulty fan motor and now with replacement aftermarket fan it works as it should. Comparing to D2 there was a lot of stuff to remove to get to it but it was easier overall. Also drawing comparisons I can say that on D2 when it failed the brushes were very low and commutator was worn through but on D3 the brushes are low but very little wear on commutator. Could be that copper alloy or brushes are more advanced on D3 resulting in less wear to metal in D3 or maybe somebody already replaced brushes on my D2 in the past and it had already gone through 2nd set. D2 had solar roof and fan failed about 130k, D3 no solar and 180k miles. I guess I will see if I can get replacement brushes for original motor, replace then and keep t as spare or sell on.

Slightly OT but this sounds similar to an issue I had with my very first Audi, a brand new '95 A4. Only noticeable during the colder months and when on a sweeping left turn (usually roundabout motorway onslip). Heater would be blowing out hot air and then on taking the onslip, it would blow out cold air until going straight again. Dealer response was 'no issue found' (just like all the others!)