Triggering a 555 timer IC
While what you need can be easily accomplished using a 555, in this instance - because of your space constraints - it seems a cheap 8 pin microcontroller might be a better fit.

In order to get the astable duty cycle you want, the 555 circuit will need two resistors and two  capacitors and, if you need to use the bipolar for the highish source and sink currents its output can provide,  the timing capacitor will be in the tens of microfarads for for an output high 60 seconds long.

A microcontroller will require, at the most, a power supply bypass capacitor and a ceramic resonator or crystal, or at the least, just the bypass cap if you choose one with an internal oscillator.