I don't know the 4610 as well but I'm assuming it's pretty similar to the 4000 with respect to the neutral safety switch. Double-check the parts manuals online if this doesn't make sense or post back. Should be a pair of wires coming out of the top of the shifter plate on top of the transmission. Those wires make their way up under the cowl, and there's a pair of bullet connectors in between.
As a quick test, you could unhook those connectors and put an ohmmeter on the wires heading into the transmission. If the hi-lo shifter is in neutral, you should have continuity. It's it not in neutral it should be an open circuit.
It's most likely the switch that is bad. That switch is easily accessible by removing the 10 or so bolts on the shifter cover. Put both shifters in neutral, remove the bolts, lift the cover part way to get a look at the switch. I've found it's easiest to disconnect the wires at the switch so that you can remove the shift cover completely and set it aside.
Then you can check continuity on the wires, and also on the switch itself. (Since the hi-lo was in neutral, you should have continuity on the switch at this point.)
I think from most posts here it's typical that the switch goes bad. You can get a new one from Cole-Hersee for $10-15 bucks or so. I've seen them for as much as $30. The last one I bought was no longer made in USA.. made in Mexico but still looked pretty well made. Time will tell. Might want to get a new gasket for the shifter cover too depending on the shape yours is in.
If you do decide to jumper things, keep in mind that although a car will jump and stall if you try to start it in gear, the tractor will simply start up and drive away. Plenty of torque and not much will stop it. I'll let your imagination and the posts of others drive that point home. Just be careful. I've always driven a clutch and always make sure I'm in neutral with the clutch in before turning the key. Others might not be thinking along those lines, and the cost of a mistake is high, so keep those folks in mind.
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