[AdamHeard]

In this case I think a hall effect or light sensor packaged right is a much cheaper option with plenty of accuracy.

A light sensor can be made into such a sensor by merely making the surface of your wheel an encoder disk of sorts. For example, if your shooter wheel is white/light colored, put 1-2 lines of black electrical tape on it. If it's black, do the opposite.

Far, far cheaper. You'd wire it as a single phase (not quadrature) encoder and just set the ticks per rotation to 1-2 (whatever you install on it).