As the main beam warning light works it proves the switch is working. If the wiring, connections and the bulb are also ok the light must work. That it doesn't means something is wrong between the switch and the bulb. Unless a fuse is hidden away somewhere it amounts to the wiring and connections, subject to tracing the wires using a circuit diagram.

I seem to remember old Honda model headlamp wiring wasn't quite as straightforward as other vehicles and the headlamp circuit "talked" to the charging circuit so the charge rate was boosted when the headlamp was in use.
Clearly a circuit diagram is a highly desirable aid to tracing the wiring and understanding the various functions.
Good luck!