At least on my E36 M42 both connectors (DME and gauge) are two conductors. The grounds go back to the dash or DME. I think the older E30s grounded to the block.
I am actually wondering now if the temp gauge doesn't work without the car running. The gauge is apparently heavily dampened by the DME.
Anyone know if the temp gauge is supposed to function without the car running. on a '95 318ti?
The E30 and early E36 systems are the same, with detail differences. The E30 gauge sender does only have one connector wire, and is grounded to the block. It's usually a blue body and/or connector mounted further forward in the head. Make sure you have the right part number on that sender too - those two coolant senders are different part numbers and are not 100% compatible. The E30s all have one pin on both the sender and the harness.
You have an oddball hybrid, but a Ti is more E30 than E36. That cluster is unique to your car. IMHO I'd suspect it's just an updated E30 cluster. I'd be temped to check the gauge pins going through the board, or caps on the SI board. They can die from temperature, age or just an unlucky overload.
The temp gauge won't report the temperature without power - the needle is powered by 12vdc to a small coil; the SI board should read sensor resistance (or indirectly shunt voltage) to determine output to the gauge's coil. Don't short the connector to test a sensor - it's possible to damage the driver board that way. I'd strongly recommend using only BMW's ETM (or Bosch's specs) to run tests - some items can't be tested directly without an oscilloscope and/or other exotic equipment.
Other E36 have a gauge test mode, but I don't think the Compact cluster can do that. To test those, push the odo reset button in, insert the key and turn it to Position 1 (Accessory Power).