May I safely install an external switch to the fan control in my thermostat?

Would this be the R and G terminals?


(The purpose is to have (fan only) circulation increased in the house, controlled by a digital timer that opens and closes a relay switch throughout the day/night for short 1-3 minute periods.)

I have no idea about the safety of such a added item BUT there are thermostats that can be programed to do something like that.

Check up and read about the digital thermostats at this link. Programmable stats offer this on some models. Then it will be safe.