In the mean time a technical note could be found reporting some
statistics of observations done with RS13 and RS18 sondes during the
decade of the 70s. The report mentions:

"No lag corrections were applied to the observed temperatures. It was
estimated that the lag corrections amount to only 0.3 to 0.5 degrees
Celsius in the troposphere when the lapse rate was dry adiabatic."

According to this text the time-constant would have corresponded to
about 6s to 10 s.

This would indicate that the time-constant of the temperature sensors
didn't noticeably improve between the 50s and (the beginning of ?) the
70s.