Starter will not stop engaging

Good afternoon.

The solenoid on the firewall, if you disconnect the little wire from the ignition switch, will it stay engaged?

It is possible that the ignition switch is sending current to the solenoid in the run position. That would mean replacing the ignition switch if that is the issue.

Roy

Removal
1. Disconnect the battery ground cable.
2. Remove steering column shroud and lower the steering column. Refer to Steering Column: Service and Repair: Removal/Installation.
3. Disconnect the switch wiring at the multiple plug.
4. Remove the two nuts that retain the switch to the steering column.
5. LIFT the switch VERTICALLY UPWARD to disengage the actuator rod from the switch and remove switch.

Installation
1. When installing the ignition switch, both the locking mechanism at the top of the column and the switch itself must be in LOCK position for correct adjustment.
To hold the mechanical parts of the column in LOCK position, move the shift lever into PARK (with automatic transmissions) or REVERSE (with manual transmissions), turn the key to LOCK position, and remove the key. New replacement switches, when received, are already pinned in LOCK position by a metal shipping pin inserted in a locking hole on the side of the switch.
2. Engage the actuator rod in the switch. Must be inserted in the slot of the sliding, black carrier.
3. Position the switch on the column and install the retaining nuts, but do not tighten them.
4. Move the switch UP and DOWN along the column to locate the mid-position of rod lash. Tighten the two ignition switch retaining nuts (TOP NUT FIRST to minimize rod binding) to 4.51-7.34 N.M(40-65 in-lb).
5. Remove the lockpin. Connect the battery cable, and check for proper start in PARK or NEUTRAL.
Also, ensure the start circuit cannot be actuated in the DRIVE and REVERSE position and that the engine will shut off in either DRIVE, REVERSE or NEUTRAL. If the engine will not shut off in the above positions then the switch is NOT adjusted properly.
The switch will have to be re-adjusted. Refer to Ignition Switch: Adjustments.
6. Raise the steering column into position at instrument panel. Refer to Steering Column: Service and Repair: Removal/Installation.
7. Confirm that accessories are deactivated with ignition switch in OFF position, and that accessories are operable with switch in RUN position.

Hello,
First thing I would check would to unplug the signal wire from the solenoid and see if it stops the starter. If it does further trouble shooting will be necessary however if the solenoid continues to power the starter I have seen many times the problem being a ground issue. The older Fords are very prone to issues if the ground strap from the engine to the firewall does not have a good connection causing the solenoid to overheat and stick. If you find that this is an issue you may have to replace the solenoid again as they can be damaged after this happens. Please keep us up dated on your progress and I will be glad to help you further trouble shoot the issue further if you need me to. Thank you for using 2Carpros, hope this was helpful.