I have the 56 Shop manual handy and it states:
"The cooling system of the passenger car is pressurized at approximately 13 psi."
on page 115. Subsequent pages make no mention of a cap for Thunderbirds.
Page 363 in the spec section states:
"Cooling system on all cars is pressurized to 12-15 pounds."
This section does give Thunderbird specific specs, but no mention of a different rating for the cap on a Thunderbird, but I will check other sources.