Turn on LED with the opening of a switch
Something like this should work.  Tune R1 for LED on current.  Tune R2 for your specific transistor, to get it into saturation.

Update: To save battery current, you can run the transistor not in saturation mode (make R2 even bigger).  But you won't get good repeatability from circuit to circuit as the gain of transistors can vary wildly from part to part.







simulate this circuit &ndash; Schematic created using CircuitLab