before you blame the starter,check your grounds thoroughly, and I mean unbolting the connectors at each end,if you can,peel some of the insulation back away from the connection,if you see corrosion on the outside of the wire braid,replace the entire cable.
electricity travels around the outside of each wire in the braid,not through the wire itself,so you end up with high resistance.
if you see where there is evidence of arching at the connector,usually black fleck looking spots,and or corrosion,clean those.
the switch can be suspect also,are you turning the key the same amount of distance each time??? try different key positions to see if you can replicate the issue.
it could also be a neutral switch problem,rock the shift lever when it does this,does this clear it up?
to test the solenoid,jump it at the terminal marked (s) be careful here,depending on how its wired,that terminal may be grounded when the key is engaged,usually the case when volatile fumes are involved in a closed environment,(like an outboard motor when gas fumes can be present.) use a test lite here to verify.
the bad part is that it is an occasional problem,and they can be the worst until you have a complete failure.
if you need further help,pm me, I work on this stuff everyday.