post a pic.. does your tractor have a thumb sized button on the trans cover, tht has a lil wire that runs to one o fthe 2 small terminals on the solenoid, with the other one run to the key switch?
if so.. the one from the thumb button is a ground.. and the switch may be bad or the wire chaffed.
pull this wire off the solenoid and see if it still does it.
heck.. the solenoid itself may have it's main contacts welded. if you pull all but the large wires and it still does it.. pop it with a hammer and check agaon.
post back.
ps.. keep her in neutral and clutch blocked during all this testing.
also. is this a sos tractor? they are a tad different than the plain gear models i just described. also possible a prev owner REALLY changed the wireing..