How to detect movement of gadget without electricity

Microswitches are available in a range of formats, are very small, are mechanically simple and very reliable.

Figure 1. A selection of microswitches.

The lever types are very sensitive so little force is required to operate them due to the lever's mechanical advantage.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 2. Wiring is as a simple as using the normally-closed contact (which will be usually open when the weight of the container is applied to the switch).

A vibration sensor switch can be built or bought using a spring, wrapped around a central pin.

When moved, the spring contacts the pin, closing a circuit. Gravity alone isn't strong enough to close the circuit. They are surprisingly effective in all dimensions, not just in the axis perpendicular to the pin.

They are available in a variety of sensitivities and constructions, including bare and enclosed. I have seen versions made of just coiled steel wire soldered to the board.

Source: Adafruit

Similar to Solar Mike's suggestion, these avoid any energy usage while not triggered.

Should the unit be stored in a dedicated holder, a 'NC' type magnetic reed switch would suffice.

The reed switch could be mounted in the unit and wired in its supply line.

A magnet, located in the holder, would keep the reed switch open.

The reed switch would close and the unit would power up, on retrieval from it's holder.