For an accurate 60 second pulse, a 555 timer won't be sufficient.
There are two ways of doing this to the desired accuracy:
1) Use a crystal resonator (high frequency, say 32kHz), then divide this down using a ripple counter. Most RTC chips produce a 1Hz square wave from a resonator, so would require a divide by sixty circuit.
2) Do what the motor did, and get timing from the mains. Transform the mains to a suitable level (say 5vac), produce a square wave using a schmitt trigger (60Hz in the US), then use two divide by sixty circuits to produce the desired pulse.
Andy