My guess is that it still just needs more cleaning and oiling. When I got my 401a, it would not zigzag at all. If you will take the top off and watch as you push the needle bar back and forth, you'll see all the things that have to move freely for it to zig zag. Stuff in the "nose" has to move as well as several levers between the needle bar and the cam stack.
There are several threads here on cleaning and getting everything to move on a 401a. There was one by archaic arcane that was really good. Here is the thread from my journey with my
401a https://www.quiltingboard.com/vintage-antique-machine-enthusiasts-f22/401a-problem-t288873.html
It references several other threads that are really good. It sometimes just takes a while to get everything loosened up. The 401 has tight tolerances, so old dried up oil can stop it from moving correctly.
bkay