Electronics

Electrical is not my forte, but with a good service manual, my peak voltage meter, and some probes I can usually pick my way through this stuff. While I kind of grasp what you are saying here, forgive me if I seem skeptical. The reason for that is while the green/red wire in the harness for the gear position switch loses ground when I turn the key on, BOTH of the green ground wires at the ECU do NOT. I back probed those, and used the same ground as when I tested the neutral position wire. This is one of the items Honda lists in the trouble shooting for no peak voltage at the coil.

Looks like he's dropping ground to the coil.   Pretty much replaced everything electrical on the machine except the wiring harness. 

This is a carb'd, air-cooled 2011 500.   Not mine.  I've been trying to help him troubleshoot it.

Nope!  This one isn't mine, just trying to help him diagnose a 2011 TRX500FPM (footshift with power steering)

In case this is useful.... a member recently measured a new OEM ignition coil (2010 420 Rancher) and provided us with the specs. I think your model uses the same part number... Resistance between the two primary winding terminals on the coil should measure around 2.75 ohms. Between each primary terminal and the end of the spark plug cable should measure around 18500 ohms (18.50K ohms). Between each primary terminal and ground (the stack of metal plates on the end of the coil is ground) and between the end of the spark plug cable and ground should all measure open circuit.    If the coil measures close to those specs try running a jumper wire from the positive battery post to the Red/Black terminal on the coil with the coil still plugged into the harness. See if you get spark.   You may have to recheck the peak voltages on the CKP and at the coil, make sure that one of them haven't failed since you first tested them.   The ignition switch is a suspect in my mind. I've seen them fail intermittently and under load, opening the ignition like yours was doing after a few minutes of runtime.