Yes, choke is tapped offf 'run.'. There are only so many outputs from the key switch
1...ACCESSORY, hot both in "run" and "accessory"
2....RUN or IGN1....hot ONLY in run, goes dead in "crank."
3....Start...hot only in "start" feeds and triggers the start relay, nothing else
4....Bypass or IGN2....Also hot "in start" but a separate contact and goes to coil + side of coil. This is the ignition power source for "start"
If disconnecting the choke "fixes" it I'd say you are there. Frankly I'm not intimately familiar with "what all" is a choke. I know there is a heater, there may be a radio cap (which can short) and the OEM setup has that odd thermal timing device, and surely it can develop problems.
