Welcome aboard, RetroJoker.

The mechanism is similar to the attached diagram. (not drawn to scale)
There are two vertical supports (green) for the control panel near the left-rear and right-rear corners of the control panel.
When you push in the drawer (purple), two pivot-arms (red) attached to the body of the table keep the bottom of each vertical support from moving back with the drawer.
Rounding the bottom-back edge of each vertical support will smooth the transition.
Scott
EDIT: If the hinged mechanism is too complicated, use the approach in this video. There's a good view of the drawer at 1:27.