I also have an older 2005 Timecutter as well
You may want to try by passing the seat switch:
(If 2 wires under the seat, un-plug the switch and run a jumper between them)
Also:
https://jackssmallengines.com/jacks-parts-lookup/manufacturer/toro/riding-products/74360-timecutter-z4200-riding-mower-2010-sn-310000001-310999999/electrical-assembly There's not much wiring to the machine, popping the main fuse is odd, with your circumstance.
If the seat switch by pass doesn't do anything, follow and check all wires for a short to ground.
Also, the lever safety switch for each handle are somewhat flimsy. Make sure both switches are fully seated and the switch is working when the arms are moved..
Check battery cable connections as well as to the starter relay. A loose/crappy connection
could pop the fuse
.