I'm having an issue with my fuel gauge going to empty when it's full , then reading accurately once it hits half full .
I know there's a problem with sulfur build up on the sensor(s) from other posts .
Are there two separate fuel level sensors in the fuel tank ?
Is there one on one side of the tank and another on the other side that register full to half then half to empty ?
I really don't want to replace both sensors if only one ( I believe it's the passenger side ) that needs to be replaced .
Any help would be greatly appreciated .

 

I was only aware of the float on the pump under the drivers side back seat. But now I see there is supposedly one on the pass side too and the computer averages the two readings.

To run E85 at my horsepower level I had to install a GT500 Dual Fuel pump last year... did everything myself. It’s not that crazy if you want to pull out your fuel pump and look at it. Could also be an opportunity to upgrade the pump (new one will have new float sensor) if one were so inclined.

I assume it’s no more difficult to inspect the sender on the pass side. Maybe if you look at both you will see that one of them is binding for some reason.

 

Here's the fuel tank exploded () view, which shows the fuel pump, left side, and the fuel sender, right side. Both have senders. The right side is connected through the 'valley' at the top of the tank to the left side via a tube, the pump draws from whichever tank has fuel, nominally both at the same time.
http://iihs.net/fsm/?d=319&f=Fuel%20...ded%20View.pdf
You access either side from under the rear seat, which comes up fairly easily. Two rubber covers come off and the sender/pump can be serviced in the car. Obviously one should take care to not have fumes hang around and/or have a spark around because explosion potential, so be careful. Have a fan or two blowing fresh air in the car, and keep the tank as closed as possible to prevent fumes from escaping. There, the lawyer should be at least somewhat happy now...

http://iihs.net/fsm/?d=40&f=Instrume...luster.pdf&p=3
That's the electrical regarding the fuel senders on a 2005 Mustang. One per side. Except... well, there's that third connector and resistor, looks like, involved. And the whole set of circuits are spliced to heck and back. Very confusing. This is for any of the cars, 4.0L, 4.6L, 5.4L... This is an instrument cluster wiring diagram specific to the fuel level and some other things. So I'm not sure.

For comparison, here's the 2011 version.
http://iihs.net/fsm/?d=711&f=060%20-...luster.pdf&p=3
Notice how there's two distinct runs? One for the sender on the fuel pump module, left side, and one for the fuel sender, right side?

Yeah. Something doesn't make sense on the '05 to me...

Anyway. Yes, there are two. And you can confuse them, or rather the instrument cluster computer what does the fuel level, temporarily, by doing donuts or just hard enough cornering, while on a half or less empty tank. The fuel will slosh into one side or another, or the car will get a false reading due to the sloshing. Whichever the event, the averaging of the fuel levels in the two saddlebags will result in an bad level, so all of a sudden you're out of gas. It will clear up, but it takes a bit of time, as the sampling rate is not very often in the grand scheme of things. Source: Do this time to time in Awesome when I'm just having too much fun with her amazeballs suspension setup for taking a '90 degree' turn at 40 MPH. (No, serious, she does that. It's hilarious scary fun, but of course, I wouldn't ever do that on the streets... Kids, don't try this at home, ask your parents before ordering, not applicable in Toledo.)

All that to say, it *may not* be the sensor... unless you're not driving wildly, then yeah, it could be one or both. Or whatever that resistor may be, can't say that one even makes sense... You might can try to test the senders out of the car, but at that point, might as well replace them both. And get Motorcraft new, because yeah, you could save money, but... some jobs you don't wanna do twice or three times because cheaper parts, eh?

Hope that helps, and welcome to the forums!