I forgot that I had run out of Campari but my cocktail robot was already pouring a Boulevardier so I swapped the Campari tube for Zwack and now I have a cocktail that is not what I was looking forward to but is okay #whiningontheyacht
I ran the tubes through the pumps, and up the top to form a faucet. I tested them all with water. The nice part of this design is all of the electronics are suspended above the liquor bottles, so I don't have to worry about any drops falling onto the circuits.
I formed the faucet shape by bending a wire to the shape I wanted, and clamping it to the cabinet with a wide washer. I ran the tubes along the wire and ziptied them.