Sorry, don’t mean to resurrect an old thread, but I was looking for the same and figured it out on my own. I wanted a script (or scripts) to invoke, rather than just an automation; for those who follow, see working config below:
Ranunculales. Does your fan remain on until you manually turn it back to auto? I have a similar automation but my Nest reverts back to auto after thirty minutes.
The Nest API has a fan duration setting but the HA climate service does not. I suspect Nest or HA is defaulting to a 30 minute duration, but I have no way to change it.