You shouldn't need the voltage reducer.
"
The fuel and temp gauges will work on 6 or 12 V and are not polarity sensitive."
https://www.ctci.org/battery-for-6v-to-12v-conversion/
The original gauges & senders are effectively self-regulating.
They work on current flow and heat, not voltage. (image below)
IF it's necessary, "a 10 ohm 10 watt wire wound resistor" may be preferable to an
electronic voltage regulator.
That said... if you have voltage to one Temp gauge terminal and ground the other terminal the needle should swing across the gauge face. If it doesn't work the gauge usually has an 'open' circuit, a broken wire inside. An ohm/continuity meter should show you the same result.
The gauge may or may not be reparable. Sometimes it's easy....
A dash gauge repair shop may be an option.
Keeping oem style gauge & senders together is preferred to replacing one half of a pair with a reproduction part. The reproductions may not work accurately when combined with the old King-Seeley style gauge hardware from the 50's.
If you do need replacement parts try to find working used originals or NOS.
The '55/'57 T-Bird parts suppliers have replacement gauge & sender pairs for 12v conversion of 55's.