I had exactly this same problem, my fuel pump top hat broke at the two support points and the entire fuel pump assembly was dangling by the wires in the gas tank. This didn't allow the sender arm to reflect the fuel level accurately.
Apparently it's a somewhat common issue in these cars, and CJM actually makes one out of billet aluminum to prevent this point of failure. That's what I bought to repair mine instead of installing a new plastic one that will end up breaking again.
Since you're going to be checking the sending units anyways, you'll know if you have this issue as once you unscrew the cap the fuel pump won't be attached to it (well, it will be - but by the hose/wires)
Thankfully it's pretty easy to work on the fuel pump in the Z, I'd recommend checking the passenger side first as that's where the pump is located and you'll be able to identify if the top hat failure is causing this!
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