Upon further review I think the answer is no. The panel appears to be the same "fawn" color as the rest of the interior on a 1962.

The above based on photos of a surviving original '62 C10 Custom Cab:

http://i645.photobucket.com/albums/...uck%20Stuff/1962Interior_zpsb07d2286.jpg

http://i645.photobucket.com/albums/uu176/lakeroadster/Chevrolet%20Truck%20Stuff/1962_zpsb05ec00e.jpg

http://i645.photobucket.com/albums/...Truck%20Stuff/1962Engine_zps9f68f7ee.jpg