Mac mini stops blinking in standby
I am not sure if it is only with the most recent model, but apparently by default it is set to go into deep sleep after a few hours, and this turns the power light off entirely.

This thread on AVForums provides a command that should disable deep sleep, if that is what you want.

pmset -g
sudo pmset -a autopoweroff 0


After entering this it will prompt you for your password.