2015 jeep renegade taillight ground corrosion

Hola GRM, I have an electrical question. Not my  area of expertise, so talk to me like I know nothing lol. 
 

My girlfriend has a 2015 Jeep renegade latitude. The driver side taillights, reverse lights, and turn signals are all out. The cause (as far as I can tell) is a shorted/corroded ground wire from the wire connector to the tail light housing. The filament in the bulbs is not blown, and no fuses have been blown. Here's some pictures I stole, from another forum where someone else had the same problem. 

Connector with center pin (ground), burnt up. 

Housing with same center pin problem

 
So, I can buy the new housing, and I can get a new connector and solder those wires in, and hopefully fix it.  
 

However- what would have caused this? And is there anything else I should be checking? 
 

Thanks in advance guys!   

Not sure if you can get the pigtail,  kind of hit and miss on Fiat cars. I would  check the body ground and load test it before putting new parts on.

I wonder if you could cut the housing open and run a new ground wire (bypass connector) to ground and reseal it with RTV. Cheaper than new parts.

That failed because the connector pin is too small for the load it carries. Do the repair Donebrokeit suggested above if at all possible.  

Thanks! Will try that and report back 

Yep, follow Donebrokeit's wise advise. I'd also go over every single ground you locate while you're at it.

Bad design.  Very common these days to want a 1mm connector to carry ten amps.  Also, very stupid.

Solution is either a box of new parts, or getting into the light assembly so you can solder on an independent ground wire which you would then connect to the wire on the other side of the melted connector.

"Very common these days to want a 1mm connector to carry ten amps. Also, very stupid."

I agree. Seeing hair thin wiring on vehicles made since 15 years ago or so is very disappointing. That and difficult to disconnect connectors can make electrical/electronic work a real pain (connectors are made to withstand WW111, while the wires wouldn't last through a walk in the park). Meanwhile, I was told by my Nissan dealership (while buying new vehicle in late 2019) that the single heaviest "component" group of some late model vehicles are the electrical wiring and electronics.

In reply to Streetwiseguy :

So, what gauge wire should I use? 
 

if I run it to a stud/ground it near the taillight- should I go thicker gauge? 
 

or should I just match the gauge used? 

I would go larger. 

so, thicker gauge down to this ground point? 
 

I have a ring terminal that would fit there  it's much thicker wire- 12awg to be exact. 
I hate electronics lol. It would be about a 2 foot run- is there any problem on grounding too many wires to one place? 
 

sorry for all the questions- I hate electronics lol 

The wire itself doesn't really need to be any larger than stock.  The connector overheated because it wasn't making a perfect connection, so if you can solder onto the ground in the light and run it down to that ground stud, you should be fine.

Also, this isn't electonics yet.  It's just electrics...

My first foray into soldering went well. All the lights worked, and I learned a little about wires- the crap wires I bought from Amazon in a soldering kit fell apart in my hands so I got some good stuff from autozone, and now all the lights work! For my own memory- I used 18ga wire 
 

thanks for the help guys!