Need a circuit that lights a LED but shuts down LED after a while
Can you use a SPDT switch for the garage sensor? If yes, how about the circuit below?

It uses a MOSFET. The gate is almost no current so you do not need a ginormous capacitor like you would in your circuit.

When SW1 gets thrown into the up position (garage door fully open), M1's gate immediately goes to 9V because C1 is discharged. This turns on the LED D1.

C1 starts to charge through R1 and the gate drive to M1 slowly drops until finally LED D1 will shut off.

When SW1 is thrown into the down position (garage door begins to close), 9V is disconnected and C1 is discharged through R3. Also, R3 limits the current to prevent arcing which would shorten the life of the switch contact.







simulate this circuit &ndash; Schematic created using CircuitLab