Why is my indoor A/C Blower randomly turning on and off only with Nest?
The battery is likely depleted and it's pulling a small amount of power to charge the battery. This signal is causing the blower to turn on momentarily. The fix is probably to run a common wire, preferably to the A/C since that's where Nest expects it in a dual transformer configuration (which I assume you have since both Rh and Rc are connected).

Hopefully your A/C control board has a common terminal, and an unused wire. If not, you can use a Venstar Add-A-Wire.