the PATS (Passive Anti Theft System) light will blink steadily about once a second or so, when the key is out of the ignition, indicating a properly working system.
wheny ou turn the key to the ON position, it should illuminate and remain for about 3 seconds, or so. Once started, it would go out completely while running. Explain the differences of yours from that, minus the starting part obviously. lol.
I would look in to corroded/cracked/splitting wires going to the starter, starter relay, or the ground from either.