I have a similar configuration and also disconnected my fuel pump to verify the primer solenoid activates. Yes, I definitely hear a clunk when I push the primer button, not as loud as the master or starter solenoid but a definite clunk.
I assume your wiring has 12 volts coming to the primer button from the switch that turns on your fuel pump. Also, the primer button should then provide 12 volts to the primer solenoid when the button is pushed. The other side of the solenoid should be connected to ground. It’s possible the primer solenoid plunger is stuck in which case you would not hear a clunk. You can verify the wiring by verifying the magnetic coil of the solenoid by holding a small screw driver close to the solenoid and have someone push the primer button. You should be able to detect the solenoid becoming magnetic when the button is pushed. If the solenoid becomes magnetic and still no clunk, you should be able to disassemble the primer solenoid valve assembly and determine if the plunger is indeed stuck and possibly free it up.