John Deere have a habit of changing the wire colour at every switch which can make tracing a wiring fault real easy ( if you have the schematic ) or near impossible if you don't.
So pull the plug off the key switch, and jump the B ( battery ) and the S ( start ) terminals with a short jumper you will have to make.
Make a 1/2 dozen of them & keep them handy, about 2" to 4" long with male spade on each end plus a couple about 18" long also with a male spade at each end.
With the key switch jumped you are energizing the cranking circuit which will make testing easier as your 3rd hand can hold the beers.
Now pull the PTO switch plug.
If you have a manual one, check for 12V on one wire and jump it to the opposite wire ( FLAT SIDE not EDGE wise )
If it has an electronic PTO this is a bit more problematic as there may be 2 wires with power to them.
If there is no wire with power then you have found the problem, a broken wire between the key & PTO switches.
Do the same for the brake switch.
Usually JD also use a start relay so you might need to jump it or bypass it.
To be on the safe side, pull the kill wires from the magneto or just disconnect the engine gang plug that has the kill wire in it,
Doing things this way the engine will not start as there will be no power to the carb solenoid which is fine cause you are looking for a fault in the cranking circuit.
When working on a live circuit I like to use a test lamp rather than a meter