If it was the ignition switch, you wouldn't get the oil light either.

If you can make it happen 20% of the time, you can fix it: Open the hood. Get back inside the car and flick the ignition switch to position II four times, then once more to get the condition to recur (20%). While the key is on, and only the oil light on, stare at it a moment, daring it to fix itself.

Just to be clear, the car is not running, but the dang door alarm is driving you nuts.

Assuming it stays broken, slip out of the car carefully, so it doesn't notice. Peek back at the cluster to verify the oil light is still on, all by its lonesome. Grab your trusty sleuth-meter or test light and ground the negative probe reliably. I use the braided jumper between firewall and cam cover.

Then with your positive probe, look for voltage, first on the alternator's housing. If nothing there, run around quickly to look at the lights, and ensure the car isn't trying to fool you by fixing itself once again. If there is voltage on the housing, well, you know you need to fix the ground wire.

If the problem remains stable, the next place to look is at the D+ terminal (exciter wire) on the alternator. Try not to disturb the wire connector, but touch the probe to the alternator's terminal. The end of the screw itself, rather than the tab, would be a good probe spot.

If you see battery voltage there, but still not on the alternator housing, you can indict the alternator (regulator assy, connections to it, or field winding). If no voltage, then quick, check the lights again to make sure the car hasn't wised up to what you're doing. If the problem is persisting yet, breathe a sigh of relief and wiggle the connector at the alternator.

Now, if that didn't change things, you're beginning to suspect that "exciter wire" and all that is in the path back to the cluster. Simply removing the connection from the alternator and grounding the exciter wire now should light the lights, and when they don't light you've proved the problem lies toward the cluster.
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Art Benstein near Baltimore

Don't be irreplaceable. If you can't be replaced, you can't be promoted.