Originally Posted By R. Belmont
For the two-timers solution you'd start the second timer in the service routine for the first one. It's a fairly common pattern in MAME/MESS.

To me, this seems like a good use case for some sort of 555 device. It would manage two timers and one output line, generating a fixed PWM pulse train. Simple to implement, but given how commonplace the 555 was, it might prove useful.