back in the day when i first got my 85 mk2 supra....i use to have that problem too...i found out wat cause it....its the wiring from the steering to the horn next to the washer fluid tank....i got a cut/broken wired.....because...that wire is touching the body frame so thats what it cause me that trouble...but i dont know about your...but if i were you...i will double check the wiring from the headlight and follow up and see if you saw any uh....wiring that it connect wrong...what i mean wrong is that...sometime you rewiring it wrong...for example... you switch the red into the black n the black into the red so thats why it goes opposite when you start the engine.... correction if i wrong...