Audi A4 B5: Wipers Acting Erratically After Ignition Key Turned

I have such a problem that after turning the ignition key the wipers start immediately, wave several times and stand where they feel like (sometimes they will return to the place where they need to be - lottery). After pressing 1 pulse or washer similarly; they wave and stand where they want a few times. I thought it was a wiper motor ... BUT
- when I press the 1st gear it works once in a while and returns to zero position
-2 run slightly faster
-3 gears operate quite briskly and return to their zero position

However, after turning the levers to 0 they fly several times and again stand where they want.
The feathers are ok and there is no resistance during work.

I thought that the wiper module may be 377 (under the steering wheel), I undressed, cleaned the contacts of the relays. But it did nothing. I bought a new module but it's still the same .... I don't have the strength. I don't know if it matters, but there is a rear window wiper switch on the lever although I have a sedan without a rear wiper.

Car data Audi A4 b5 sedan 2000, petrol 1.6

While trying to fix and search for the cause, I accidentally damaged the electrolytic capacitor in the relay module (including the one under the steering wheel). To my surprise after switching on the ignition (and even starting the engine, the problem disappeared).

There is probably ALEE ...
While everything is OK at ignition, after the engine has been started and the gear has been turned on and off, or one impulse has been started (one turn of the tour machines, they have to wave several times anyway.

What the hell can be ??
I give pictures of this module after taking it apart


Is it possible for me to buy a damaged module in the store (new - on my order)? And the question is what is this capacitor for ??

@ Nikusert
The capacitor in the old module (relay) fell off and it started to be ok. But not for long
Today, when inserting clocks and checking another failure (no fuel), I accidentally started the wiper handle. And same thing again....
Since the wiper motor is not easily accessible, can it be checked from this shelf under the steering wheel? I can use the meter anyhow.

PS. Can this wiper breakdown and lack of fuel status display (float ok) be associated with a computer failure?

It happened suddenly.
In general, the car was functional with this handle. I don't know if this has anything to do with it but it all started when I switched the rear window switch. However, I don't want to let go of any problem in any configuration. It was a calm day but today I have switched again because the problem is back. I have no more strength for this car
I am a little afraid to take this handle because I know (I exchanged the handle from flashers and lights in audi80) that here you have to throw an airbag and I'm afraid that if I fold it, it will explode somehow while driving
How do you look at the wiring harness from the rear window switch? can you cut it ?? Does the Audi a4 avant (wagon with rear window) have one relay module for windows or 2 pieces. Maybe the module is stupidly looking for this wiper and is "sucking" on the front?
I already lack ideas and strength. I would happily go to an elek specialist. but large queues (up to 1.5 weeks a week) and good rates. PLN 100-150 per hour of work. Reading your suggestions and a bit from the forum regarding the engine, on average I see it in his guilt because on the run he returns to the correct position - timeout also works approx.

@ Nikusert
I thought that all the electronics in this module are relays under the steering wheel (pictured above), and in the engine something like a tacho shield with contacts.
But it doesn't give me peace that it all started after using the rear window wiper switch. Apparently repaired (up to 1 day ok) and then the same after switching.
For now, I will give up the divination of coffee grounds and go to the doctor electronics. If someone from Wrocław sits here, reads it and does it, please go to Priv (please provide phone number)
I will definitely share what was wrong

Sorry, Is this a contact shield or electronics (integrated circuits, resistors, etc.) ?? Maybe a silly question, but I did not play with electric car so much - I deal with household appliances repairs on a daily basis
Another stupid question on my part ... I don't know anymore which position of the rear wiper is gear 0
I certainly checked in all positions, unless I missed something and I don't know about it yet.

Added after 11 [minutes]:



And how to cut it ??

The limit switch in the engine turned out to be guilty. A little swinging so I didn't feel like playing with her. The cost of the new engine is PLN 180. Thank you all for helpful hints