The switch as described previously is shown here. This method was used on the majority of stylophones.
It is the underside of these that need to be cleaned.

To get at the metal plates for cleaning, carefully remove the circlips from the pegs using a thin knife blade.

The switch in pieces, ready for cleaning. Make sure the plate - which will drop out easily - goes back the right way up.

The 'clicking' sound of the switch is made by the notches passing over these ridges, moulded into the plastic case of the stylophone.

This model shows 'real' switches fitted to a stylophone.
It is unlikely that they will cause a problem.
This is a bonus, because on this type they are soft-riveted to the case, and would be far more difficult to repair - or replace.
A squirt of electronic contact cleaner into the workings should be enough to get things going again, should switching be the fault on this type.

Switches (trouble - Part2)