One side of the fuse is +12 volts and the other side is the load. In parallel with the fuse is a resistor and an LED. The fuse normally shorts out the resistor and LEC so there is no voltage across them. If the load shorts or draws so much current the fuse blows, there is now voltage across the resistor/LED and it lights.
The awning drew enough to blow the fuse and light the light but then you took you finger off the switch which removed the load. Now there's no voltage across the LED because no current is flowing in the circuit. Hit the button for the awning and you'll see the LED light.