Is this normal for the fuel gauge?

Not normal. Does the temp gauge do the same thing?'

FIRST order of business is to FIND THE DRAIN

Take a test lamp and hook in series with the disconnected battery ground. Remove fuses one at a time and see if the drain goes away. If not, disconnect the alternator output stud and see if that kills it.

The temp gauge seems to always work.

I'll try that w/ the test lamp tomorrow if i can.