Display Name: Chuck Van Dusen
It may very well be that you have a failing ignition switch (key switch) since power to the solenoid has to pass through it TWICE, but it could also be the other safety circuits that must be in the proper state to allow the solenoid to be powered by the key switch. The basic wiring for the starter is shown below:
Since you have an early tractor with a P218 repower, you may have either a separate solenoid as was used on the original B series engine, or the solenoid-shift starter that is common on the P series engines -- depending on if the dealer notched the frame for the later style...
In either event, you will not have the brake switch in your harness. One place to look is for the neutral switch to be working as it should...try holding the hydro speed lever firmly toward the steering column in the notch in the slot. If that is the issue, that switch can be adjusted -- instructions are in the TM1590.