I'm not sure but I suspect this may be a case of the wish being father to the thought.
I mentioned 'ti' because that is the mnemonic name BMW gave to the injection time signal from the DME should a gentle reader find themselves perusing the BMW Electrical Troubleshooting Manual.
The clusters are
very similar, but to be sure, I would probably have to spend a day or two comparing the instrument cluster section drawings in the ETMs. I think I wishfully read that into the "etc" in the opening post, or that he had swapped in the 328i wiring, when the OP wrote:
... I used the dme, ews, etc from the donor if that makes any difference.