I doubt that the computer system and its cue modules that "wake up" and "educate" Pal Mickey needs to be switched on and off on a daily basis.
I'm pretty sure it could just RUN most of the time.
The system MAY have a "standard procedure" as part of any of the park's "Open" vs "Closed" protocols. Meaning that if the Park is "at all" open to guests, certain things MUST operate... lighting (both practical and "effects") and background music come to mind... as basic "atmosphere" minimums.
I would think that IF the Pal Mickey "cue system" was ever turned off... it would NOT be when a park had guests present.
(Our Pal is still quite chatty with park info an hour or so after the scheduled closing times.)