Staircase Timer with On/Off switches
Figure 1. A pneumatic time delay-off switch typically used for stairwells. This model is for the British standard wall box.

There are no electronics. You press in the plunger which closes the electrical contacts. The plunger is pushed out by a spring at a rate determined by a pneumatic bleed valve which controls the rate that air re-enters the piston. When the button is close to fully out the contacts are opened.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. What you've got and what you want.