Troubleshooting 4066 as a button hack
If you want to use a bilatheral switch between two circuit boards then you need the two boards to share the same ground otherwise it won't work.
Bilatheral switches are most well suited for switching an analog voltage/current, What I would do is I wouls use an opto-coupler, it has an internal infra-red led and a photo-sensitive transistor for its output, you can connect the transistor output across the switch and activate it by driving the led from the other board.

It is generally a good idear to use an opto-coupler when connecting two circuit boards the way you are describing because that way you keep them electrically isolated from each other.