Well here is my two cents,

My fathers 99 3.0L did the same thing and ended up being a bad alternator...BUT...that being said, you can keep starting yours you say, so it may not be the same problem. Also you would probably have a low voltage light come on.

Had a similar problem with an old Town Car, ended up being the ignition control module on the distributor, but can't recall if the 3.0L are coil pack or not.

It is electrical, not fuel related. That is for sure. Fuel is either on or off, no in between 90% of the time.

Wish you the best of luck!

 

I thought it was my alternator too. When I crank it up and it run for it's 5 mins, I checked the voltage with my multimeter, it read 13.3-13.1. I thought this was gonna be a easy and cheap put back together job but it's taking alot of my money and time to get this thing running. The ignotion coil is $50 the wires $50 and the plugs are $30. Also my radiator fan now stopps because its rusted around that bearing.

 

If you were closer to me I would give ya one. I have two here from a parts van lol.

I would defiantly have an alternator test done at a shop, they will put a load on the alternator and see if it needs replacing.