Hello Madmodders. My first post here, so may I take this opportunity to thank HS93 for guiding me towards such a nifty forum.
For anyone interested, here are a couple possible circuits for the Useless Machine gizmo. The first is designed around a bog-standard 555 timer chip, while the second circuit is a simplified version, albeit it means you have to modify the servo for continuous rotation (remove the gearing end stop, remove the internal circuitry, connect the two motor wires direct to the DPDT).
Happy modding.