The “SPST latching push-button switch” is either on or off, right? There is no momentary contact or break ability, right? When it is OFF and you press it down it clicks and changes to ON and stays there. Right? Then does the reverse when pressed and clicked again?

The driver needs a momentary disconnect in the power supply leads to the driver in order to switch between Low, Medium and High, or Low, Medium, High and strobe. That switch you have probably does not permit that. Perhaps if you press and switch the light off and then back on rapidly enough you may be able to make the brightness level change. If you can not do that with the switch you should be able to make a brightness change by quickly disconnecting and reconnecting one of the wires in the power circuit.

The driver is meant to be used with a reverse clicky switch as is found in many off the shelf tube lights that have tailcap switches.