If the Bike runs its working.
The only time I hear the start up clicks of the fuel pump is after the bike has sat 12-18 hours, the pump repressurizes the system. The fact you do not hear clicks most of the time is good, it means your needle valve and seat inside the carb
are sealing properly. My bike used to give a couple of clicks every time I turned the key and eventually got to the point it was idling poorly, I had to replace the Needle Valve and seat, they were leaking and this can be attributed to ethanol in the Gasoline in my less than humble opinion.
Go ride it.