So for the last few months we've been building a car for NASA Spec E30 and after a ton of work she's almost ready to go back on the road but we've hit a wall trying to wire up the tachometer to the instrument cluster. In particular we're trying to find the wire that plugs in here;

at the back of the instrument cluster to feed data to the tach. From everything I've read on the net this seems like a common problem but I'm yet to get a definitive solution.
One poster I saw suggested that the wire may be located here;

about 3' down from the computer on the wiring harness. The BLK/GRN wire goes to the transmission and is a position sensor from what I can tell (the car temporarily has an auto tranny while we're building a separate M20/Getrag for competition). The other two wires are BLK/WHT and PUR/WHT and did not send tach response after testing each with a lead to each of the terminals on the back of the cluster.
So far I've gone through a stack of BMW manuals and every .pdf I can find on the wiring and can't find any mention of this wire or it's convention. My worry is that we may have inadvertently removed the wire while eliminating the non essential parts of the wiring harness (i.e. environmental/window controls/etc.). And before anyone suggests it, the issue is not the batteries for the cluster.
Thanks in advance for any help and let me know if there's any further data or pictures I could provide to help diagnose this.