I wouldnt bother with that much complexity, you could do that with a relay and 2 push switches or microswitches, arrange the switches so that one makes when the sraw is open and the other when the draw is closed, the relay operates and latches on when opening and when open the switch is operated and the relay drops out closing the draw and restarting the cycle.
The draw open switch would be normally closed and the draw closed switch a normally open.
It would be simple still to just use the switch you allready have, cut aslot in the platic section of the draw and position the toggle switch insode it, make the slot the right length so that the switch is just made when the draw is fully open and just made when the draw is fully closed, the system will then oscillate nicely, without any electronics.