This is programmable. I use it in another vehicle to "push" a momentary button to turn off auto-stop. It activates 30 seconds after ignition power (for me) it can be momentary or latched.
https://www.amazon.com/gp/aw/d/B07BT32T1M?tag=wranglerorg-20
Get the correct part for the drivers side. NAPA, quadratec, any auto parts store. Then assemble like the pic posted over there, at the other forum, where you posted the same question.
I cut the lowest speed wire. I could never tell when it was on at thst speed anyways. I don't remember the color. (Then I put black marker over that speed marking on the dash)
Just for grins, unplug the electrical connector on your ignition switch, to kill it. I am wondering if it might be your ignition and just a crazy coincidence.