Just bought a used Singer 20u73, needle slightly off ce Sewing Machines Parts and Sales in Los Angeles

I just picked this up on the weekend as my first sewing machine. I got some square mazes printed out and was starting to go over them with just the needle to get the hang running stitches.

I don’t have a picture (I can get one when I get home) , but the needle is slightly to the left of the centre position, about 1-2mm. I can move the needle to the left all the way, and when I move it to the centre position it is just slightly to the left. If I fiddle with it a bit I can make it go dead centre, but I can tell that the little slider isn’t locked, and after 20 or 30 stitches it slips back to being just slightly to the left.

Any idea where to start with diagnosing the problem? The instructional manual didn’t seem to have much regarding that. I will take it to a shop if I have to, but I have plenty of tools and time so I’d like to get familar with maintenance myself if possible.

Cheers!