It's not a ground issue.
At every key-on, start sequence, the gauge control module and the gauges do a handshake and check-in. If one or more gauges fail to sign-in during this initialization, those gauges will be completely ignored for that entire run duration. (There are no further attempts to handshake until the next start sequence.)
As many owners have noted, a lower-than-expected-battery-voltage will occasionally disrupt this hand shake and when this occurs, one or more gauges may be "dead" for that entire run duration. In these scenarios (low battery voltage), the GT's alternator will be full-tilt charging the battery. Therefore, turning the car off and then re-starting it will usually remedy the problem.
If your fuel gauge is not working - and it hasn't worked across multiple start sequences (whereas the other gauges have) then the problem is entirely unrelated to a ground issue, it is simply a failed gauge. Call Autometer, order a replacement gauge (~$260), plop it in and you're done.