I doubt your head light switch is causing this. With that said, (DISCLAMER ALERT). It is hard to diagnose without actually seeing the problem. If you have a “bad” tail light bulb it could cause these weird problems you are talking about. The tail lights are dual filament bulbs and if one filament touches the other it causes weird effects. If the running lights are on, the power can back feed through the touching filament into your directional and hazard circuit and vice versa when you use your brakes, directional, and/or hazard lights this can back feed into your running light circuit. Remember that one filament in the tail light acts as the running light and the other acts as the brake, directional and hazard functions. This may also occur in one of the front directional lights also. They have dual filaments also and fill the same roll except brake lights. If you hit the brakes do both dash directional indicators light up and stop flashing or one or the other come on solid? Does this happen with the directional on or off? This may happen with the head lights on or off. Try it both (all) ways. If so that points to a “bad” tail light bulb or front directional bulb. If not a bulb I would suspect a bad turn signal switch. The cat whisker contacts in the turn directional switch are also known to cause weird things like you describe. The turn signal switch has the brake light circuit and directional circuit running through it and also isolates the front lights from the rear lights so when you apply your brakes the front lights don’t light up with your brake lights. If I remember correctly, if you have your hazards on and you apply your brakes, all four corners, and dash indicators will come on solid. Bottom line… Check you bulbs first (read replace them, they are cheap and can be used as spares if not the cause of the problem). Again try replacing all your dual element/filament bulbs first.
Hope this helps, John