Occasionally I get the "gearbox fault" on the dash when I first cold start the car (2001 VDP) and if I shut it off and re-start, the message goes away. No trouble codes and the car runs fine. I also get the "check rear lights" when apply the brakes, and all the lights are working. Any suggestions? Windshield washer pump not working/not making any noise and fuse is good. I assume the motor/pump got fried due to some poor quality washer fluid that froze in the tank. Do you know if the washer pump from Autozone (aftermarket) will be worth installing? The OEM one costs an arm...and half a leg. Thank you!

 

The washer pumps are made by VW you can buy aftermarket ones on ebay. You may have to alter the wiring to connect to the new pump, a couple of spade ends sweated on and shrink tubed should do it. I'd check the pump with a bench battery first to see if it's a gonna, water inside it that freezes can crack the pump head body leading to water getting into the lower part where the motor is.
The lights, check the connectors into the light housing, pull the carpet back and undo the connectors, squirt a bit of wd40 on them and a bit of wire wool on the spades. It could be oxidization.
Oil levels on the gearbox are critical, has it had a change/check at all? I'd see if it's up to level.