Our Lemax Tilt a Whirl and Ferris wheel are located such that the control boxes are in hard to reach area. So I finally decided to extend the cables. And here is how I did it.
I bought the ubiquitous flexible 3 conductor red-black-green cable like used to connect Atlas HO switches to their control boxes as well a four foot white 1/4" diameter heat shrink tubing.
Cut the Lemax control box cable about a fourth of the way up the total cable length from control box end, not critical though you want to have enough wire length to easily manipulate when soldering. Carefully remove about 1.5 inch of cable covering at each end, avoiding slicing the tiny conductors. You will see three thin volume control wires and two heavier power leads. Mine were green-yellow-blue volume control, and white-gray power wires, but your colors may be different, just insure three skinny and two heavy wires.
Cut two (2) four foot pieces of three conductor wires then peel off the green wire from one piece to create the red-black power cable, the other piece will be the volume control cable.
Carefully remove about 1/4" insulation from the five Lemax wires and 1/4" from the two cable wire ends. Use 3/32" heat shrink sleeves to cover each joint (make sure you slide a sleeve onto the wire before you join wire ends!). As the Lemax wires are so small to twist connections, I folded the wire into a "hook" and the looped it through the new cable wire folded "hook", and touch soldered the connection. Too much heat will evaporate the Lemax insulation, so a on-off the joint is best strategy. Solder the new cable at the display end first leaving the control box to last. Jot down what cable color goes to what Lemax wires, for reference when wiring other end.
Thread both cables through the white tubing and over the sleeved connections until tubing is against the display. At the other end, measure about three inches from tubing end, cut off and discard excess. Repeat connections from cable to control box wires like above.
Test that control box turns dispaly on-off and volume control changes the music in right direction. When satisfied, slide white tubing down over control box connection, and use heat gun to shrink tubing down, if desired.