The miniature RC cars have radio control in a very small form factor. You could try tearing one down and see what you find, or try sourcing the control separately.

https://www.dicksmith.com.au/da/buy...cro-racing-car-blackorange-fs144-blackorange/

https://www.ebay.com.au/itm/404213419477

Unfortunately, I cannot find any even close to the size requirement...which is what led us away from something RF. There is a picture above...but I have about half of a sphere that is 20mm across at the widest point with the center already being occupied by the motor and the base already occupied by the battery and an existing mechanism that is required for marking the type of monster. It really doesn't leave much room. Right now I've purchased some IR components, reed switches, magnets (a few different types and sizes), a few RF detector ICs to see what I can do with them. I did find a RF receiver that would do the job perfectly, but is just a little bigger than I can manage space for no matter how I try and move things around. (11mm x 18mm x 5mm)

 

I’ve been trying to find it, but I’ve used a Hall effect switch that is activated through 1/4” of air with a 3mm x 1.5 mm rare earth magnet. These may be small enough to fit in a figure. You may must already have power for your motor. You could address electromagnets beneath the playing field arranged in a matrix to activate any figure by its coordinates.

I like the thinking and I had considered something 'under the board' to make it work, but the board has many shapes and sizes and I think that would be too much 'setup' to try and make it work nicely. Right now I think my best strategy is going to be IR sensors/emitters .. but I definitely still open to ideas.

 

I like the thinking and I had considered something 'under the board' to make it work, but the board has many shapes and sizes and I think that would be too much 'setup' to try and make it work nicely. Right now I think my best strategy is going to be IR sensors/emitters .. but I definitely still open to ideas.

What do you mean by “many shapes and sizes”? And “setup”?

 

These are the smallest 433MHz transmitters and receivers I can find.



You can get these smartphone vibrator motors on the surplus market.
Remove the asymmetric weight and you will have a very tiny motor.

 

What do you mean by “many shapes and sizes”? And “setup”?

The game has 150+ missions. Each mission uses any number of 'room tiles' that are all varying shapes and sizes. Some missions it might be 4x50, some missions it might be 20x20, some missions it might be a giant letter T making it 50x50-ish. You don't really know until you go to set up that mission.

Also, we just play on regular tables, and not always the same one, so having some electro magnets under the game surface for me to control would be difficult. It does make me think I might be able to get the 'magic' effect I'm looking for if I just have a really strong rare earth/electro magnet, that I can pass by on the bottom of the table to trigger a toggle on/off system. Like the 'magic ring' idea that was mentioned earlier...but from under the table.

 

Ok, so the HX1838 is an IR receiver that is ~5.4mm square (plus leads). Here is one Amazon Listing for the component. This listing also includes a remote for use with the receiver.

It can be used with an SMT ATTiny85, which is also ~5mm square to interpret the IR commands. Here is a source from Mouser for the MCU.

These might fill your requirements.