96 XJ fuel pump won't turn on unless 'new' CPS is unplugged.

96 XJ with 4wd and 5 speed.

Here's the parts replaced run down.
-Fuel pump relay
-Fuel Pump
-Cap, Rotor, and Pick up assembly
-Ignition coil
-Crank position sensor

Fuses are all in good condition, wiring is checked, no damage to harness and continuity from fuel pump to relay and PCM.

My issue is that when the XJ sits overnight the fuel pump won't turn on the next morning unless with the Jeep off I unplug the CPS, then turn the key and the fuel pump will prime the engine. I can then plug in the CPS and the engine cranks right up. If I then turn the XJ off, it will function normally again. Something is 'resetting' to a point where it reverts back to a no-start situation. I haven't driven it for fear of being stranded since I replaced the CPS with a new NAPA sourced part.

Any ideas as to what can be causing my issue?

Try disconnecting the battery for a few minutes to reset
everything.

If that dosen't work, then there's an ASD relay that might
be causing your problem. I believe it's in the relay center
under the hood.