On a non Jeep vehicle, Audi Q7 TDI, I had the same problem.
Turned out to be battery drain when sitting overnight or longer.
In my case it was drawing power from the AMP.
By the time it started the alternator would charge the battery up again and everything looked good.
I determined the battery drain after I purchased a voltage checker and started checking the battery voltage afternoon and mornings, or after the vehicle had sat for a few days. It was dropping to low 11’s from memory.
Not saying you have the same problem, but worth looking at.
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Jeep TJ rebuilt 4.0L, Custom Steel Roof Racks, vintage ((Jeep specific)) 15” Centerline Hellcats,
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