Shelburn,
I have a Japanese made DIAL 'n SEW machine that is very similar to yours. It's needle parks to the left when on straight stitch too. I've found off set straight stitch and satin presser feet for it at my local sewing machine shop. Mine is also takes long shank feet which complicates finding them.
It too makes a beautiful straight stitch and a wonderful zig-zag. No cams and it only has a couple adjustments for varying the stitches.
It too was a rescued machine. My wife found it tossed out on the curb for trash pick up after a yard sale. Snatched it most quickly. All it needed was a bobbin case and some glue for the damaged wooden case. Easily done.
These are excellent machines. Not fancy nor modern but with proper lubing they'll last three lifetimes.
Joe