As you note, there is no binary pressure switch in the system. I added one in my system when I changed the compressor. The brown wire is direct from the thermostatic switch to the compressor clutch. The power to that switch comes via the black jumper from the fan switch. The yellow is the 12V supply to the fan switch. The black wire goes to the fan. The fan must be on for the clutch to engage. No relays. If the power is intermittent, there is probably an issue with one of the switches, or it's just the thermostat operating. A 12V test light would be an easy way to troubleshoot. Also, make sure that someone hasn't mixed up the wire locations on the switches.
BTW if you ever need to replace your compressor, I highly recommend an aluminum replacement for the A6. Dimensionally identical, bolts right in, more efficient and about 20 lb. lighter!