In one of your earlier posts you stated "...the bell button contact across the LED with the series resistor shorts the LED out and full current then flows into the solenoid striker for a ding dong chime bell". That implies a different wiring arrangement than I had assumed. The attached diagram is my best guess as to what circuit connections you meant. Please confirm if this is correct.
At a quess, id say that was assumed BEFORE you posted a pic of FIVE terminals on the switch.
Normal 2 connection pushes the led goes off when the push is pushed