We might be looking at this differently which is what I'm trying to understand.
There are two windings on the Bally flipper coil (4 wire ends).
Thrust winding (short thick wire) deep inside around the bobbin, and hold winding (long thin wire) over the thrust winding.
Thrust winding on the side lug connects to ground via the flipper switch.
Other side of thrust winding ends on the middle lug where the hold winding starts.
Other side of the hold winding ends on the other side lug that switches to 43 volts.
These windings in total are connected in *series*.
F14 Tomcat apparently has Parallel wound flipper coils. Looking at the F14 Tomcat flipper schematics, both the thrust and hold windings connect at power and switch to ground which tells me they are indeed parallel connected.
Now I know nothing about games post '84 but look at the schematics... Or is there some other magic to parallel vs serial wound flipper coils?