Why not install equipment in the tower cab (to be active on the night shift) that would sound a loud klaxon if the controller fails to key his mike within thirty seconds of receiving a call?
This is a stop-gap measure at best, what about sleep inertia? If the controller is sleeping on duty then waking him/her up and expecting an 'instant' decision might be worse than letting him/her sleep... I remember a mate of mine who had an incident around 2am where the pilot was suffering from sleep inertia and reported the wrong level, despite being questioned multiple times...
I have worked in a few ATC locations with different approaches to sleeping and staffing during night shifts. Where I currently work is an excellent way to work night shifts, but the shifts are still fatiguing (short turn around into two nights). But I would imagine that managers are disgusted about the 'waste' of man power.
My previous employer had a $$$ only approach to working nights, it was/still is a crap way of working nights, it was not unusual to see multiple sleepers while on duty at various stages throughout the night. I've never seen it in my current location.
Applying (regulated) duty hour rules and proper fatigue management to ATC shift patterns is the only way forward (as airlines/regulators should be dong with pilots), we know so much more about the science of sleep but the $$$ always get in the way of managing it properly. Too much "when I was a controller" thought processes regarding attitudes to night staffing from management levels in ATC.
Closing towers and making the CTAFs is one solution, not a good one at most locations, it doesn't address fatigue issues in 'Area control or approach control' locations.