If this is a on a nearly new car then let them put the new headlights on and you confirm that they work before you take the car back.
If it was me dealing with an awkward garage like that I would say that I'm not prepared to pay anything until the problem is fixed completely; then if it is wiring causing the problem they'll need to fix it.
A smaller backstreet garage would be much better for a problem like this.
I had the same problem with one headlight on a Honda years ago. Replacing the headlight lamp did, in fact take care of the problem. Do yourself a favor, and use genuine Honda parts.
Have you replaced the bulbs yet ? Seem to me that would be the final answer in your quest - if it still is an issue take it back with the receipt for the bulbs and request your money back for the diagnosis since it was wrong. Sometimes a complete diagnosis requires multiple tests after one is fixed - it is not always cut and dry as it seems - they diagnosed as far as they could - prove them wrong.
NEVER go to a mechanic or dealer that charges you a "diagnosis fee". That should be free! Hopefully they didn't tell you about that upfront. If they did (and especially if you signed something, which I assume you did), you owe them the money.
If they keep changing the headlights and if you jiggle the wire and it comes on. CHANGE THE CONNECTORS first. its shorting out it's either that or the wiring but chances are that it is the connectors. I have seen that before
Ok ok
Headlights going on and off for 8 months, sometimes the left one, sometimes the right one. They always go out and come back on.
All the guys at Honda keep saying is your headlights are burned out. But I giggled the wire last week and got them to come back on. But they keep cutting me off mid-sentence and saying "SIR!!! I TOLD YOU THE HEADLIGHT ARE BURNED OUT. TAKE THE DIAGNOSIS OR LEAVE IT, BUT EITHER WAY YOU STILL OWN US $115 FOR THE DIAGNOSIS FEE."
Customer service in American is dead and I am sick of it!!!!
