[V8] on a mystery hunt

[Roger M. Woodbury]

Oh yee Audi fools and experts!  Here is a puzzment.
 
For a couple of years we have enjoyed guessing at the fuel remaining within
the tank of my wife's 100CS Avant.  I have adopted the procedure of filling
the tank every three hundred miles, and then carefully checking the amount
of fuel added against the mileage on the trip meter.  The car gets a very
consistant 21-24 miles per gallon and has for 140,000 miles.  
 
The fuel gauge registers nearly full on filling and then at about ten
gallons consumed is on the empty peg and by the time around six gallons or
so remains the "tank empty" ikon is lighted on the warning panel.  
 
The logical conclusion (one reached in consultation with thou almighty
Audiguessers last year) is the tank sending unit has failed.  That has been
the opinion of my wrench also.  
 
BUT, at the same time that this has been going on, the coolant temperature
gauge is registering zero also.  For a long time it has registered very low,
but now doesn't move off the peg.
 
We have had all the builbs in the instrument cluster replaced recently.  But
I am wondering if this might be a ground problem in the instrument cluster
itself...just old age corroding the ground points for the fuel gauge and the
temperature gauge.  No other instrument issues.
 
Comments?  
 
I am reluctant to throw a fuel sender at the car until and unless I am sure
that will cure the problem.  Is there a test procedure short of opening the
top of the fuel tank?
 
TIA
 
Roger