Here's the thing about those shifters...
They have a lot of moving parts with surfaces that are supposed to slide past each other. I can tell you now that yours are all rusted up, and probably not working correctly.
Remove it, take it apart (it's not difficult at all), clean up the parts with a wire wheel or something, throw copius amounts of grease in there, and reassemble it. You can make it work again if you try. They probably wouldn't ever quit working in the first place if they had provisions for periodic lubrication.