How the heck to I remove pins from this 14-pin power connector?

My house is absolutely not grounded well. I actually have another thread pursing this same general issue from the grounding side! Every outlet in my house reports "open ground" on a test tool. The outlets in this bedroom specifically don't even have a ground wire to the box. I ran a ground to a cold water line, which made the test meter happy, but didn't affect the problem. I rent, so installing proper grounding isn't an option. I could run a ground line outside to a stake, if that would actually work.
 
That looks pretty plausible. How’d you find it?
From this picture (SP10 power cable connector) Google directed me to AMP TE CONNECTIVITY 206044 1

Screenshot 2023-10-09 at 20-45-40 DSC_0467.jpg (JPEG Image 1600 × 1070 pixels) — Scaled (45%).png


https://www.digikey.com/en/products/detail/te-connectivity-amp-connectors/206044-1/19361
 
There are pin extractor tools designed for that, otherwise it's impossible.
There are many kinds and sizes, but it has to be exactly the right size for the particular connector.
The mfr part number should be somewhere on the connector, possibly it's an Amphenol circular connector.
If you damage the pin, you will need a much more expensive mfr spec ratcheting crimp tool to install another pin.

An example, but this may not be the right one. You need the mfr connector part number to find the proper extractor.
https://www.amazon.com/JRready-Extractor-Removal-Connectors-Connector/dp/B0B6FMZMH4/ref=sr_1_5

True. When you order the connectors the come with the pin pulling tool. When I was in the hardware side of the house, we'd order thousands of the connectors... the configurations were different but the pins proper only came in a few "gauges". So, we had tons of those pin puller tools in our tool boxes.

You will need to figure out the part number on the plug assembly.