OK, last time. "What we got here is a failure to communicate" (Cool Hand Luke, 1967). If you really don't understand how these things work you had best just use the device exactly as called for by the manufacturer with exactly the parts supplied. Otherwise you could end up with an unregulated pressure vessel between your legs. I would not consider sink cabinet doors adequate protection.
That said, if I were going to do this I would rig up some way for the beer faucet to activate a solenoid valve to serve as the cold water supply valve that feeds the tank. There can be no restriction in the beer faucet Perhaps a tiny magnet inside the faucet and a reed switch just outside but hidden by the tower. The switch and magnet must operate a boiling temperatures. Use a 12VDC NC valve powered by an NEC Class 2 wall wart plugged into the garbage disposer receptacle. This would be a lot of work, probably require machining some special parts, probably destroy the original functionality of the faucet and tower, probably leak, etc.
Another option would be to mount the entire tower on some type of pivot so when you pull on it a switch is activated under the sink and opens the solenoid valve. Unless you were very clever, this second method would almost certainly allow water to leak from the sink deck into the cabinet below.
As in a earlier post, why bother?