Finding the correct wire
Seems like a standard doorbell, though your "pressed button" status seems like a probable measurement error.

For detecting the doorbell button, connect to black and white - if that does not work, connect to black and red. The reason I'm pretty sure you have a measurement error is that if black and red are 0V and red and white are 12V, black and white should be 12V, not 0V.







simulate this circuit &ndash; Schematic created using CircuitLab

Or, if black and white are 0V, and white and red are 12V then black and red should be 12V - Same circuit as above, swap labels for white and red.

So one of your measurements is probably not what you've said.