Inspired by this circuit; https://everycircuit.com/circuit/4793352077443072 by EC user firstmoon
Made me wonder if something like this could be done with relays only, no active devices.
The first relay is a latching relay activated by the pushbutton. This also provides the switched output to the load, in this case a lamp.
The 10000uF capacitor begins to charge via the diode resistor and pot. The second relays function is to reset the timing cycle. The second relay operates at 9V and when the capacitor reaches this voltage, the second relay operates breaking the current to the first relay which was routed to ground via the normally closed contact of the second relay. A 10R resistor is also applied across the capacitor to hasten the discharge in preparation for the next timing cycle.