04 Explorer a/c burnt?

I have a good one for you! I knew sooner or later this would happen.It could have easily burned and totalled the vehicle.
My son's 04 Explorer which was having earlier problems with the a/c compressor not powering on, now it is a bigger problem. Previously he was jumpering directly from the a/c clutch wire connector to the battery, to engage the a/c compressor clutch with Automotive Air Conditioning Repair
Well,he decided to hook up a toggle switch to the suv interior. After doing that, it wasn't long before the a/c clutch two wire connector shorted together and caused melted black electrical tape and the toggle switch to burn up, taking out the battery in the process.
He had to replace the battery and now when he tries jumpering directly to the battery again,it just causes sparking.
My question is the a/c compressor clutch coil
possibly shorted out or could it be the old original wire connector itself causing the arcing? How can you test the a/c clutch coil?
I am presently trying to locate and buy a new a/c clutch wiring connector pigtail. It is a two spade/two wire connector. I called A/Z and Oreilly's and they either don't have it or unsure which connector is the proper one.
I may have to call a local Ford dealership.
I do understand all of this is a bone head way of powering the a/c compressor and shouldn't have been done.
Does anyone know a part or oem # that would help to find the correct replacement wire connector.
That is the first priority right now and then get it repaired properly at a mechanic shop.
This 2004 Ford Explorer is a 4 wd, 4.0L V-6, with Vin K
I just need to replace the wiring pigtail to eliminate a possibly burnt out/grounded out connector and hope that he didn't burn out the a/c clutch coil. I would appreciate your help with this very stupid problem.

Response:

1).. reminds me of putting the penny behind the fuse... or in modern times, tin foil around the fuse;-)

2)The A/C clutch coil is an electro magnet. Knowing that I suspect that the Compressor itself is probably bad causing excessive heat by dragging on the clutch surfaces. And I have seen the compressors start fires.

UPDATE
The 04 Explorer meltdown was when the vehicle wasn't running. It shorted out with the a/c clutch wire connector (where hot wired)the two wires touched. So I don't really think it was the compressor itself involved. It was operating well when jumpered due to inability to energize thru the OEM control system via the clutch cycling switch.
Can I check the a/c clutch coil with a multimeter for continuity and/or Ohms? I read that continuity would confirm a good complete circuit. I just want to get the car back to the point of a/c compressor able to engage properly and then get it repaired properly at a local mechanic shop.
I did call a Ford dealership and found a new a/c clutch wire connector pigtail.
Thanks guys for your assistance, will update you later.