1996 25HP Merc electric start - will just click when trying to start

So of course was looking at buying a bigger newer boat and went out fishing with our 25HP Merc electric start. Out on the river and fishing then go to move and the motor just clicked. Pull the motor to start and starts right up, turn it off and starts with the key no problem. Fish again for a while and same issue.
Am I wrong to thing solenoid? I replaced starts in most of my vehicles int he 80's and early 90's so to me that is what is sounds like. Is there a way to test the solenoid? Battery is fine.

Thanks

It would be interesting to put a voltmeter on the battery cable at the solenoid and see what the voltage is when the problem shows up, the most likely reason for a click and no start is not enough voltage to do the job. The easiest test for the solenoid is if it has proper batery voltage and voltage at the wire from the key and doesn't work then it needs help. Consider these things though, the source of a starter that acts up could just as well be
1) a battery that isn't as good as you think it is,
2)a bad battery cable connection at the battery, solenoid or the starter and this includes a defective connection between the cable and the terminal at the ends
3) starter switch going bad (not as likely here but you never know)
4) a starter that is starting to give trouble due to worn internals
5) a poor ground connection that is not allowing enough juice to get through (similar to #2)
My advice is use a voltmeter and test to see what the available voltage is at the various places before you start throwing parts at it, if it is just a poor/corroded connection it won't cost anything and if it really needs a part it will be money well spent and not wasted.