Starter engaging with ignition "ON"??

Have a 93 Crusader 454XL. It has an ignition toggle switch with a starter button. When I turn the switch on, the starter engages then cuts out when the engine starts. I do not have to press the starter button. I have disconnected the power wire from the switch to the button, taking the button out of the loop and it still starts. What would cause this and why would the starter cut out after the engine fires? If I disconnect the yellow/red wire from the solenoid, the starter does not engage but I can hear the fuel pump running. This should not happen. Could it be the oil pressure switch for the fuel pump? I'd think if that would fail, it would fail open not closing the circuit to the fuel pump? It's just a mystery why it would engage and cut out when it starts. It's not the ignition switch because I swapped it with the working one from the port side.

slave solenoid, or starter solenoid

Bt Doctur said:

slave solenoid, or starter solenoid

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Both were replaced. Yellow/red stripe wire remains hot when disconnected from starter solenoid. Could it be the oil pressure senor for the fuel pump? It has a yellow/red stripe wire, purple and black. Purple is ignition, yellow/red stripe is for starter and black I'm assuming is just a ground.

Someone got creative with your wiring. Typically, with the key in “start” the starter should turn and the fuel pump should run (powered by the starter circuit). With the key just in “on” the fuel pump should not run (nor should the starter run). Once the oil pressure comes up (engine starts) the pressure switch closes and the fuel pump is powered by line voltage. Sounds like someone wired ignition switch voltage directly to the fuel pump which is resulting in current backfeed through the pressure switch to the slave solenoid and powering the starter. When the oil pressure comes up (engine starts) the pressure switch stops flowing current to the slave solenoid and the starter stops turning. If this makes sense, glad to give a more detailed description of how to properly wire your system. Should be able to figure out how to use your switch and button setup if you prefer that over a more conventional key switch system. Good Luck.
FL Panhandle