This remote probably uses one of those mercury cell batteries. Being that it has been several years since those batteries were taken off the shelves, I'd say this battery has been in this remote for a long long time! Ya never know... it might clean up nicely.
No one else seemed interested in this remote, so I went ahead and got it (even though I don't have a set to match it up with). Perhaps this means I will soon find an RCA remote set (wishful thinking).