I still don't understand exactly what you want. A diagram would help.
What I think you mean is that you want a relay to pulse when the on/off switch is set to "on" and to pulse again when the timer expires.
How long is the delay? It may be possible to use a relay timer.
Note that the circuit I posted was for a laptop powered by the 12V from the car electrics. Thus the ICs have to be protected from the alternator spikes. So if your device is not going to be powered from a car, truck or motor bike, then the circuit can be simplified, ie. the 6.8V Zener diodes and associated resistors can be removed.
In short, I need a better explanation.