Oh, now I understand what you want. A time logger circuit, that tracks
the time the tilt switch is on.
This is a complete different story. For this type of thing you really
need =TO READ= the tilt switch status, while the tilt switch also has
the function to latch power to your circuit.  I have a solution using a
simply 74HCT00 that should interest you, we used it in one of our "time
loggers"... similar to what you want.  Let me check if I can post public
the circuit.
Wagner.