I'm quite sure the additional terminals are there for other applications and these switches weren't just for Camaros.
However, maybe you do have the wrong one. What part number?
Also, the switch needs to have a good ground to the dash. Some switches have a ground spade terminal on them, Camaros relied on the ground bracket being sandwiched by the mounting nut when installed. (UPC 12-B2) Perhaps this could be why your dome light isn't working..?