I finally understood what was wrong. My own reconstruction of what happened at some point prior to my lathe purchase, is as follows: the missing spring holding the lower bar (see picture) broke or was lost. Because of this, the lathe would not turn on. Then the dumbass who was fixing the lathe tried to rewire the starter. To no avail. Then he or she inserted red plastic blocks into the size 0 starter, therefore fixing it mechanically to be always on.
When I realized the nature of these red plastic blocks, the fix was obvious: remove then, rewire the starter for a single non-momentary switch, and use a spring to fix the original mechanical problem. I was very lucky, because I had a nice coil spring assortment (pictured).
So, as of now, the problem is fully resolved and the ON/OFF/BRAKE switch works great!
More pix at