My house has a back-up Genset for emergencies using an auto-throw transfer switch.
Just how we could apply a timer into the mix is a good question....a simulated power failure would kick the genset on in my case.
Let us know what you come up with.
Don't know a thing about what I'm about to say but seems logical.
Splice a timer on before the power to the genset and when the timer turns the power off to the gen switch, the genset should think the power is out and kick on.
disclaimer: IM NOT AN ELECTRICION