Your Morse 1000 should be a good machine if the cam stack isn't cracked - never run it cold. I am betting it is in dire need of cleaning the mechanism that the zigzag rides on. Push on the needle bar and you will see where it goes back and forth then look under the lid and see if there is another place where it rocks back and forth - probably gummed up with 3 in 1 oil or just plain old dried up oil. I don't know if you can learn anything by looking at the stuff people have posted on the Singer 401... I just cleaned some old Japanese zig zag with that very problem - I got it to move - use some Tri-flow. Denatured alcohol will dissolve it (and the paint) - use VERY carefully. Mine still has gummed up control knobs - stuck like in cement. I think I need to apply some heat so they will move.
http://www.quiltingboard.com/main-f1...ml#post4795016
Look at window #22 on that post - there is a pic of a zig zag needle bar all gunked up. Look for something similar on your Morse.