Sounds correct to me.
I had that problem several years ago so I made a temporary repair, which worked so became permanent.
I got a small black box and an on/off.on switch from RadioShack. I mounted the switch in the black box, wired the hi and low beams to the "on" positions, and attached the box to the handlebars so that the switch is where the OEM hi/Lo switch is using a small eye-bolt and a cable tie. It has worked brilliantly and also has the added the ability to turn the lights off.