Relay for Electric Choke

The factory powered its electronic chokes from the field circuit of the alternator, NOT the ignition.
A relay is pointless. What you need is a thermal limiter.
Tap into one of the field wires, run it to a limiter and then to the choke itself.
Simple and foolproof.
I have tested, factory limiters for $25 shipped.

The field and the ignition amount to the same place, electrically