On the '66, the control unit sits behind the dash just to the left of the glove box. Removing the glove box cardboard (is it cardboard in the '62?) gives you access to the box. That's one heck of a lot easier than removing the entire dash pad, which also gives you access. The dimmer cable plugs directly into the box.
Happy motoring,
David
'91 K-Imperial driver '66 LeBaron dual air and every option known to man