I would honestly wire on an H4 plug if yours doesn't have one, it's cheap and easy, just touch brown (usually ground) to the headlight ground wire (prob green) then just use the other two wires to touch leads and figure out what is the high beam and low beam wires. Tag or write wiring down in owners manual/service manual. Proceed with new headlight enjoyment.
On the standard American system, the front flasher bulbs have an additional element that is constantly on, and acts as forward running lights. So what you are looking at, is most likely power loss to the flasher unit, either via the indicator switch, or at the flasher unit itself …….