Aaaargh. That's still not what I was expecting.
Let's try something else. Locate the ASD relay in your underhood fuse and relay box. Pull the relay and look at the base of the unit.
It should be marked with numbers like 30, 85, 86 and 87. It might not be (the wiring diagrams were different in the early Dakota years, so the relay might not show these numbers).
What I'd like to do would be to jumper 12v to the ASD circuit (same one that feeds the coil) and see if voltage on the control side of the coil still drops with everything connected.
To jump 12v to the circuit, locate terminals 87 and 30. Jump 'em with a paper clip or something.
If the terminals aren't marked on the base of the relay, the two terminals you'd jump would be across from each other. One involves the odd-direction terminal and the one right on the other side of the pattern.
Then you'll need to backprobe the grey-black wire, turn the key on and see what your voltage is. With power supplied to the coil and the engine not cranking, the voltage should be equal on both sides.