Checking into ABS wiring from module to instrumentation cluster due to this fault.
01203 - Electrical Connection between ABS and Instrument Cluster
31-00 - Open or Short to Ground

First look makes me think someone been there before. The wiring at the main connector to the bosch 5.3 abs module is wrapped in black electrical tape & has a zip tie holding it to the connector plug. The wrapped wiring goes out-of sight down toward the firewall, so if it's not stock (which I expect), previous owners had the entire wiring harness removed & likely screwed it up.

So my question for any of you Audi C5 A6 folks. Can you take a look at the wiring going to your ABS plug & comment if it looks the same, with electrical tape wrapping & ziptie?