The law requires, as quoted above, that the pilot have a means to determine the quantity of useable fuel in each tank during flight. A dead gauge is indeed accurate when the tank is empty (actually, the law requires the gauge to read empty at the unusable fuel level, not totally empty) but the rest of the requirement obviously requires the gauge to be working and giving a reasonable indication of fuel level.
§91.205 Powered civil aircraft with standard category U.S. airworthiness certificates: Instrument and equipment requirements.
(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.
(b) Visual-flight rules (day). For VFR flight during the day, the following instruments and equipment are required:
(9) Fuel gauge indicating the quantity of fuel in each tank.
§23.1337 Powerplant instruments installation.
(b) Fuel quantity indication. 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 §23.959(a);
§23.959 Unusable fuel supply.
(a) The unusable fuel supply for each tank must be established as not less than that quantity at which the first evidence of malfunctioning occurs under the most adverse fuel feed condition occurring under each intended operation and flight maneuver involving that tank. Fuel system component failures need not be considered.
(b) The effect on the usable fuel quantity as a result of a failure of any pump shall be determined.