[quote author=Geek Emeritus date=1614466738 link=msg=4910792]
I would start with a G4 channel 3.3V solid state relay[/quote]
I would not consider a SSR for switching buttons - an AC version (as you linked to) even less so. It's almost guaranteed to not do the job. A DC SSR may work, but in that case you can probably also use a MOSFET, far cheaper and smaller.
Mechanical relays will work regardless of polarity of the button. They just make and break an electrical contact.
If you know in detail how the buttons are wired, you may get it to work with a transistor.