The model Ts pretty much switched to battery, generator, and starter systems in the 1919 time frame but the early set up was still available for a while. By 1923, they should have all been that way. Magneto lighting has to be in series from the switch to the the first light on the right side and then from the first light to the second with the final wire going to ground. This is the only way they will work and not short the mag out. If one bulb burns out then you lose both headlights just like an old Christmas tree light string.
The light switch is part of the ignition switch on the starter/generator cars. The magneto only cars had a switch on the firewall for lights and the horn also ran on the magneto. There could be a problem with the light switch or a shorted wire as previously mentioned and this is true for both systems. What you have will need to be tested for proper function and connections.