I don't have a short answer.  The trouble tree for finding fuel gage
problems looks for open or shorted circuits in various areas.  Depending
what is found and whether or not you find an open or short, can lead to
replacement of the pcm, instrument cluster or fuel level sending unit (which
I think includes a fuel pump).  None of these appear cheap.  You said the
gage reads high.  If you are lucky maybe one of the connectors or grounds
has some added resistance because higher resistance means a higher gage
reading.  I'd first try starting at the fuel tank and unplug or jiggling the
connectors associated with the fuel gage... plus remove and retighten any
grounds..    or just allow for the fact the gage is off.
These are approx:
Full = 245 ohms
3/4 = 180
1/2 = 160
1/4 = 100
empty = 42

repair is removing the tank and replacing the sensor, unless it is the dash
indicator.  any case, this is a $$$ item.  Unless it is way off and is not
drifting, dont waste your money.  GM seems to have problems with gas gauges.
I had a 91 grand am that went bad, ran out of gas at 1/8 tank.  would not
have been so bad except it changed to out of gas at 1/4 tank. cost me 600
bucks five years ago to replace the sensor in the tank..  my 2001 s10 has an
issue with the gauge also.  i never let it go down to less than 1/4.   Other
friends have same issue with their 2001 S10s.  I also have a 96 S10 that
reads full for about 7 gallons before it starts to drop, again, i am living
with it rather than spending the bucks to have a working gauge.

I will state that some fuel pumps will burn out when run dry, again another
design issue.  the 91 never burnt out but have heard of this happening.

good luck and if not too bad, dont bother.