Circuit movement detector
There are accelerometers that are designed with the application in mind. There are many options available out there but a couple that might be useful:


Raise an output high whenever acceleration is above a certain amount and lower when acceleration stops.
Raise output high when acceleration is above a certain amount and output is kept high until a command is sent to clear.


Both these are designed for this application to give you as simple a circuit as possible and I suggest them compared to other options but you might have reasons to need a mechanic tilt switch.