These are full blown sub compact tractors and are a touch on the difficult side to diagnose.
If you are going to keep & use the mower then spend the money & get the JD technical manual for the mower.
The PTO is usually powered independently from the ignition switch.
They are controlled by the seat switch & the PTO switch.
The funny red thing is a diode and if you mate heard it click then it has blown & will need to be replaced
Thanks for such a quick reply to my question bertsmobile1. I appreciate you taking the time to assist me with my PTO issues. Once you mentioned the PTO having a strong possiblity of being powered independently I remembered replacing the PTO solenoid (I think it was) and didn't even think to check that again. I'll have to go with what my m8 said about hearing the click and see if I can find a replacement for the diode. I'll also check the kill switch in the seat because I know for a fact it was bypassed by the previous owner so he could get off the mower without it dying.
Thanks for the solid couple of paths forward. I'll report back here when I have explored them all.