I know there is a 'proper' use of the light, since I got an infraction/violation about improper use of headlight.
But that time though, there are street lights on, and the road is sure bright so I just turned it off, then I got that violation.
I'm just curious if turning the main headlight and the bright one has any meaning, like turn signals because I'm just using them in very dark roads, also when it's raining.
The "bright headlights" are actually the main headlights. The dimmer lights are simply parking lights, and I believe the infraction you got will have been from using these rather than the real full headlights.
If it's dark and your vehicle is moving, you should have (at least) the low beam lights on.
The game has four "lighting levels":
You can see which of these is active by pressing F4.
You switch between 1 and 2 by using the L key, 3 is toggled using K and 4 is toggled using O. I'm not sure what 4 does, it doesn't seem to have an immediately visible effect. When you have the high-beam on, many of the cabs have an indicator on the dashboard for this.
Example:
The game manual has only this to say about headlights, under "Traffic Rules":
Keep your headlights on at night, just as other vehicles do.
