Need a push/pull solenoid type of device to work off a very small battery

[Bonzarelli2015]

Hello,
Any recommendations on a push/pull solenoid or similar device that can run off a small 9volt batter (or similar) with a 1/4-1/2' movement? I also would prefer for the throw to occur every minute or so to save battery.
This is an effort to fix a japanese waving cat toy's moving arm (The ones you see in sushi restaurants) The insides are no longer working but the balanced arm is. Any better solutions, I'm all ears.
Thanks in advance.

 

[Colin Mitchell]

What is wrong with the very clever circuit it contains. You will never get a more clever circuit.
It has no switches or contacts and works by the magnet producing a voltage in the coil to turn on the transistor for EXACTLY the right number of milliseconds.

 

[Bonzarelli2015]

What is wrong with the very clever circuit it contains. You will never get a more clever circuit.
It has no switches or contacts and works by the magnet producing a voltage in the coil to turn on the transistor for EXACTLY the right number of milliseconds.

Good morning Collin,
Thanks for your response. Unfortunately, it ceased to work and I do not know why. I'd really appreciate and education (I'm and EEE so I know circuits and a soldering iron) I haven't touched this one for fear of braking it further. It's an old toy with significant value to a friend.