It's a DC motor, right?
You need a collection of switches, a spool, and TWO ropes. One to lift the chain segment, one to pull it back. Put a switch at the top which, when tripped, will reverse the motor. A switch at the bottom should be set up to stop the motor. Your go button reverses the polarity and starts it back up again. So you pull it up with one rope, pull it down with the other, just as Intamin does it.
A little custom wiring, but it shouldn't be too difficult. Hmmm...you need a double-pole double-throw slide switch mounted along the lift to control the motor polarity, and a long slide-arm so that the lift mecanism will operate the switch. So when the switch is "up" the mechanism goes "down"; when it is "down" the mechanism goes "up". At the bottom you have a normally-closed lever switch so that as the mechanism trips the direction switch at the bottom, it hits the lever switch, which cuts power to the motor. A simple pushbutton bypasses the lever switch so that to dispatch the lift you push the button. It sounds more complicated than it really is. Hmmm...
--Dave Althoff, Jr.
Whose only K'Nex set at the moment is a Ferris wheel, but that is computer-controlled...