The gyro that was running down was probably an engine driven vac/ pressure gyro.
I have read figures that give 14 minutes as the time the average aircraft battery will continue to power the normal electrical load, following alternator failure.
I don't think that included deice and pitot heat.
If the battery connections fail, the time is much shorter.
Good idea to have a battery powered GPS as a back up for the nav instruments and the DI.!!!