[bestgenman]

@"HoosierDaddy" is spot on, it is on or very near the generator head (as it is sometimes called).  The leads from the generator are not long from the manufacturer so the connection box will be close by.  In the case of a Martin, it is the box holding the circuit breaker.  Remove the cover and inspect inside.  If you are familiar with a voltmeter, start the set with the cover off and measure the voltage on the leads from the inside of the generator.  BE CAREFUL since there is some voltage there that could hurt you.

I have never seen a push to stop solenoid so I'm suspecting it moves fast enough that you don't see it pull in.