Delay turn off relay
I think with Jstola has "nailed" it.







simulate this circuit &ndash; Schematic created using CircuitLab

Connected like this switch 1 when left on will run the "delay off" program,
which is really time-limited on period.  To re-start the timer this switch must be turned off and back on.

switch 2 will light the lamp permanently.







simulate this circuit

Connected like this when the switch is tuned off the delay kicks in to keep the lamp burning for the period set. Unless you can find a make-before-break switch for this position there may be a flicker during the switch-over.  Turning the switch on powers the lamp directly, but cuts the power to the timing circuit, readying it to begin the delay-off perioon when the switch it thrown back to the off position.