Fluorescent light fixture, 2 bulbs. only one is lit but if I remove the lit one the other one lights up. I put the other bulb back in and it won't light until I remove the lit one, so no matter what side it is only one bulb will light up at a time.
Usually if a fluorescent fixture starts acting possessed, the ballast needs to be replaced. So I second the comments, especially the ones about posting some pix.
To fix, you could replace the ballast, but eventually the new one would wear out and you would have to do it again and again over the decades. Or, you could search for LED replacement bulbs that fit the fixture. They differ in terms of whether they need a ballast or not, so you might have to bypass the ballast to get them to work (depending on bulb). But you wouldn't have to worry about it any more, and LEDs can be even more efficient.
Here is an example of these LED replacement bulbs, but you have to find the right ones for your particular fixture: