Reference a timing light, you don't need it at all. Just look where the rotor is pointing and pull it out. Don't turn the engine over while its out and it just goes right back in, in exactly the same spot. Chrysler distributors can only go in two ways. Correct, or 180 degrees off.
I realize you...
Does the map light come on with the dome light manual operation? You don't mention the dome light being on as well so probably not, but if it does, make sure that isn't on as well.
Your neutral safety switch is acting up. Could be a loose connection, bad switch itself, not quite aligned properly shift lever, etc.
I'd start with the connection itself first.