The Bosch ABS controller can have bad connections inside... quite common, actually, and unfortunately usually means a new module. You can buy these by themselves (separates from the hydraulic part). There are places that repair these, but my experience has shown this option to not work well. At least, not a good permanent fix.
I am actually fighting this on one of my B5s, only it is the LR sensor.
However, given your location, I would want to make double sure the sensor and its mounting hole as well as the little tab ring in the carrier is in good order and not rusty. I'd throw a new sensor on there too before I messed with the module anyway. I assume you pulled the pass through grommet out of the body and checked the wires on both sides of the connector.
FYI: the ABS module is different for ESP and non-ESP cars, and also needs to be coded a certain way depending on equipment (you probably knew that).
SAI: your combi-valve is bad. It has rotted out, and moisture laden exhaust is being pushed back up the tube from the back of the head all the way back to the pump. There are SAI delete kits available, but obviously a tuner will have to write that out of the ECU as hardware alone won't do everything. Parts prices for SAI bits are stupid expensive (not just for VAG stuff). You could probably take the combi-valve off and have the little adapto-piece welded shut and bolt it back on if you did not want to buck up for the hardware to delete it. I think a tune would be half the price of the pump alone, LOL.