Convenience module location?

[Titan]

I think you are almost there. Using a contact spray on the circuit board of the module and cleaning up the connector pins sounds spot on.
The fact that the central locking etc is back to normal and the indicators have stopped flashing leads me to think you've managed to get away with it after the module has dried out (fingers crossed)
I'll jot down some ramblings below and hopefully you can take something from them!

The first time this happened to me was on a 1998 car with the same symptoms as yourself with the indicators flashing, central locking going funny etc. I bought a diagnostics lead and downloaded Vag-com which stated the crash sensor had an error. The Audi parts diagram told me this was under the passanger seat and I ultimately found the area swimming. The crash sensor must have been short circuiting and thinking there had been an accident, unlocking the doors and getting in a right fankle. The source of the leak was the plenum chamber drain holes being blocked, so I unblocked them, dried out the module but still had no central locking or indicators.
I got a replacement convenience module from ebay for £40, stuck it on and as soon as I copied the code from the old one using vag-com everything worked.
I think the crash sensor had caused the airbag light to come on but I'm sure I was able to reset that with vag-com. It was so long ago I did this one I may be making this bit up.

The second car was slightly different. Same source of leak and symptoms but this time I dried out the unit, fixed the leak and it was all perfect. No re-coding etc required. Lucky.

The third car (you'd think I'd have learned by now......but it belonged to a friend!)
The condensate outlet from the evaporator was blocked and the module was flooded. The central locking had never worked and the indicators had been flashing when the module was wet.
This is the interesting (honest) part.
We took out the 4 or 5 plugs from the module and then opened up the plastic case to reveal a circuit board which looked a bit corroded.
With nothing to lose, it was cleaned with a toothbrush using bicarbonate of soda mixed with hot water. Once it had dried, I used a contact spray on it like you mentioned above to dry it out properly and disperse any traces of water. I cleaned up a few of the individual wires going into the connectors that had a bit of surface rust, plugged them in and everything worked again.
I can't believe the circuit board stood up to being under water for so long followed by the bicarbonate and tooth brush treatment but it did.
I'm still getting the odd bit of solder in my mouth when I brush my teeth though.....

Finally, not sure if you have checked this but I also had to reseal the pollen filter housing under the bulkhead cover on one of the cars but can't remember which one. This is normally worse if the bung holes are blocked at the bulkhead (which yours are not) but it is possible for some water to run down the windscreen and in, if the plastic bulkhead cover or the other thinner one the wiper arms go through are cracked.
If you take the pollen filter out there are a couple of bolts holding the housing in place. Remove these and check the underside of the housing. There is a rubber seal all the way round which perishes. I cleaned it up, put silicone all round and re-seated it. I'm sure Audi will do a replacement seal as well which is not as messy a job

Good luck.