Headlight plug

Any auto parts store sells headlight sockets you can splice into your harness after cutting off the old ones. But first, fix what's causing them to melt. I'll bet you're running some massively-overwattage blue headlight bulbs.

No sorry I'm just running the standard phillips halogen bulb - I did get replacements from PEP boys but the wiring is smaller and I'm concerned about overloading them - Next stop is a junkyard

Where are they melted? While I'd love to help you, i'd seriously concider asking someone in the UK club...

What the dealer proposes is significant overkill.

If the headlight is good and is no longer making contact with the plug, it means that the contact in the connector (the metal bit that the headlight connector actually plugs into) is electrically "open". It got to this state by first dissipating a lot of heat which was caused by a poor connection, either at the contact/headlight connector interface or it was a bad crimp where the contact and the wire meet. I would guess it was the latter. The heat is what caused the plug to melt.

This is not a chronic problem; it's poor workmanship that affected your car (Mazda does precious little of this...by the way). You mention in another post that a replacement connector is available with smaller wiring. If the insulation on the wire is not as thick, but the wire thickness itself is the same, then I would use the connector. Make certain that the new contacts (where it splices into the existing harness) are electrically good. If you are not sure, find a friend who is an electrician, electronic tech or someone who understands this stuff and have them take a look at it.

I suspect that this, once fixed, will remain fixed.

Ken

Should be simple to just measure resistance, either to battery plus or ground, depending on wire.

Leon

Accurately measuring in the milliohm range is a little tricky. You get into issues of lead and contact resistance. Without having a handy AWG chart to consult, the difference in resistance when you include a short length of, say 20AWG in a 18AWG harness is probably not measurably significant.

A better way would be to wire it in and see how hot it gets. Probably won't be that big a deal for a short length of "similarly" gauged wire. If it's off by an AWG or two, for a short length, it should work OK. The wire gage would be initially chosen for an engineered voltage drop across it's length to and from the voltage source, not temperature rise.

Ken