I've had this car about a month now, still in the process of fully sorting it out. Have done some basics: coolant flush & replace, new plugs & wires, fixed a couple vacuum leaks & such.

Just now after getting home from about a 40mi round trip, it kept running after turning off the ignition and pulling the key.

Not dieseling, but smooth idle as if i hadn't even touched the key.
Gauges and AC control lights still functioning. Headlights on. [Dark outside, auto-on]
Turning key on and off produced no change in idle, nor did turning it to ACC position.

After about 5 min of scratching my head asking " is going on" it shut itself off somehow.
Started back up, process repeated.

Where do i start on trouble-shooting this? Some quick googling led to either the ignition cylinder itself, or an alternator feedback issue as suspect.

I already suspect a flaky BCM due to some lighting gremlins, possibly related?