mechanical relay output voltage doesn't change
The relay contacts are not connected to the board 12 volt power supply - they are just isolated switch contacts.

If you measure the resistance between the COM (common) and NC (normally closed) terminals, you should see near zero ohms when the relay is released, and an open circuit (inifinite resistance) when the relay is operated.

Measuringing resisttance between COM and NO will give the opposite result - near zero ohms when the relay is operated.