The requirement for indications of a tank's fuel level (not just on
empty) is stated in 91.205b9, 23.1305a1, and 23.1337b.

Let me just quote these.

91.205, b9:
"(a) General. Except as provided in paragraphs (c)(3) and (e) of this
section, no person may operate a powered civil aircraft with a
standard category U.S. airworthiness certificate in any operation
described in paragraphs (b) through (f) of this section unless that
aircraft contains the
instruments and equipment specified in those paragraphs (or FAA-
approved equivalents) for that type of operation, and those
instruments and items of equipment are in operable condition."
....
(9) Fuel gauge indicating the quantity of fuel in each tank.

I did my primary training in a plane that had a right wing tank fuel
gauge that always showed less than "F" when the tank was completely
full. If the interpretation of the FAR is STRICT, I guess that means
my training was done illegally, because the gauge DID NOT indicate the
quantity of fuel in the right wing tank (ie, FULL). Rather, it
indicated less than full.

But the writing of the reg is not explicit (they get explicit in
1337b). To me it comes down to ramp checks, FAA enforcement, and case
law. I have never flown that aircraft to the end of its usable fuel,
so I don't if the aircraft I did my primary training in adheres to
1337b:

"(b) Fuel quantity indicator. There must be a means to indicate to the
flightcrew members the quantity of usable fuel in each tank during
flight. An indicator calibrated in appropriate units and clearly
marked to indicate those units must be used. In addition--
(1) Each fuel quantity indicator must be calibrated to read "zero"
during level flight when the quantity of fuel remaining in the tank is
equal to the unusable fuel supply determined under [Sec. 23.959(a);]"

So, what's the case history? How many pilots / mechanics have been
fined, had their certification suspended or even revoked because a
fuel gauge was shown to not indicate "the quantity of fuel in each
tank."

The FAA regs listed only speak to calibration when talking about zero
useable fuel. Nothing else.

If that's the only unambiguous calibration statement in the FARs then
I think that's because the FAA realizes fuel gauge accuracy is subject
to reasonable limitations. Why would they otherwise have us spend so
much time understanding calculated vs real fuel usage, especially
during cross country training for the private certificate? If gas
gauges were really accurate then the FAA wouldn't bug us so much about
learning to calculate and cross-check, and cruise charts wouldn't be
such a critical part of the POH. The recommended way and the way we
train is to KNOW YOUR AIRCRAFT through repeated measurement and cross-
checking the perf charts.

No FAA or other training manual says "Just check you gas gauge real
quick to see if you need to pull over for gas -- and make sure you
land and refuel when the idiot light comes on!"

Gas gauges provide solid value as indicators of possible leak
situations and when you are almost out (again, calibration is mandated
to be correct only at zero).

Lawyers specialize in writing that is crystal clear when they want it
to be, and subject to court judgement otherwise. I think the fuzzy
language the government lawyers used in crafting the regs around fuel
gauges was done on purpose.