Overhauling shifters

This is a vintage Shimano Deore LX shifter that has seen better days. It works, but there's a lot of dirt, grit and some rust as well. Doesn't seem like it was ever meant to be taken apart, and even if I did I'm pretty sure I'd never be able to put it back together again. Is there any way to at least try to clean it up in its current state? I really want to try and save it.