Can you post a pic of this button? I'm not aware of a bobbin push button that changes sewing position.

Regardless, it may be a gear that's broken.

there

If you're talking about that little white thing with the red circles, that's for loading and threading the bobbin. You push one end down to wind the bobbin. It doesn't move right or left, it goes up and down.

There's a lever on the front of the machine that controls the sewing position.

Do you have a manual?

I edited my reply to clarify something.

Thanks very much for answering. Yes, I have a manual that I downloaded. I just checked it and it says to "press bobbin push button to the left to engage it in winding position."

I have an older Touch and Sew and mine goes up and down. Guess they changed them a bit. Does it sew otherwise? I wonder if there's a jam, like thread wrapped around, or maybe it needs oiling.

Sorry, I'm just guessing at this point. If I think of something that might help, I'll post back.

I had an old T & S 778. Can’t remember for sure, but I think it went back and forth. There was a huge thread on them many years ago. Maybe try reading that if you can find it.