The Cobra shift assist system is only actuated when you pull it out of gear. There's a "lever" system such that the force required to pull it out of gear is applied BEFORE the system actuates.
THEN, with the pressure (either tension or pressure on the cable depending if you're coming out of REV or FWD) on the actuator, the shift plate moves to operate the microswitch momentarily actuating the ESA while there's "out-of-gear" pressure on the lower shift cable.
The ignition pulsing causing the engine to "lope" removes enough torque on the dogs to pull them apart.
This all happens in several milliseconds. (or so)
If your lower shift cable is corroded, bent, damaged etc, the linkage is sticky/rusty/jammed either on top of the engine or down in the drive, then the pressure to just move the cable can be enough to move the shift plate and actuate the ESA any time you go into gear. which may "kill" the engine.
The linkage and shift plate will "move" when going into gear..... but it shouldn't move enough to close the switch. If it does, the lower shift cable or linkage is usually the culprit.
For your engine, the linkage, cables, and switches are pretty much generic for all models of the Dog-clutch Cobra, but you may not be able to buy them new. You may have to scrounge.....(craigslist, ebay, junk-yards, etc)
There's several sites that have pictorials of parts for all the drives.
I like this one:
http://epc.brp.com/ (email not required just click "View Parts Catalogs")