Howdie - I found this post from 10 years ago. I have this problem but think the post is a little bit inaccurate as the wire off the starter relay is the one that does not use the resistance wire.
If I put 12v into one of the little wires off the starter relay my car continues to run - this wire normally losses power then you come off the start position. Any BTDT?
Make sure you are getting voltage to the pump before you replace it. I have an 85 Grand Marquis (same basic car) and it sends the full 12 volts to the pump while the key is held over to start but feeds the pump through a resistance wire from the starter relay after you let go of the key and it returns to run. If the resistance wire breaks the engine will start but die immediately when you let go of the key. The resistance wire on my Merc. is yellow and had printing on it every few inches that says "resistance wire". I have heard of blue wires on fords. To find the wire just follow the positive battery cable to the starter relay and look for a very stiff wire about 1/8th of and inch in diameter connected to the relay.