Hi,
Is the starter staying engaged until the battery is disconnected? I attached a picture below of the starting system. If you are getting power at all times, disconnect the red wire with a blue tracer and see if it stops it from engaging. That is the trigger wire from the key. Low voltage goes to it causing the relay to close the circuit and send power to the starter motor. When the power is removed from that wire, the contacts in the relay open and the starter should stop.
Please understand, I don't have the schematics for your specific vehicle. The ones I attached are for a 1985 E350. It sounds like what you have has had a different body installed on the E350 chassis, so the wiring should be the same for this.
Let me know. Also, if the start does stop with that wire disconnected, check to see if there is power to that wire at all times. If there is, we need to check for a short to power or the ignition switch.
Take care,
Joe
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Sunday, September 13th, 2020 AT 6:28 PM