If it were me, instead of installing some non-standard connector in the TM to power the portable fridge, I would consider installing a USB-C port. In contrast to the legacy USB-A ports you have, they can provide a wide range of voltages, which you can select based upon the cable you plug in, and can supply 100 watts.
I would be looking for a version of this that could supply 100W
to a single port:
https://www.amazon.com/Outlet-Built-.../dp/B0C6TJTKH4
Here's an example of a device that supplies 100W through one USB-C port, but instead of getting hard-wired in, it just plugs into the cigarette lighter socket:
https://www.amazon.com/Charger-UGREE.../dp/B0B3CSLPZR
You may be tempted to use that, but in my experience, such a connection is weak, and so at higher currents gets is fairly resistive, causing heat and excess current drain. So I'd really prefer one that is hard-wired,
especially if you're planning on drawing anywhere near 100W.
Then to select the voltage you desire, you'll need a trigger cable specific to that voltage. Something like this, where you'll see there are 12V, 15V, and 20V options, but that is rated for a higher current (these are only rated for 5A):
https://www.amazon.com/2-Pack-Jacobs.../dp/B08NRM6X2Y
If the supplied barrel plug isn't appropriate, either find a different cable with one that works, or just cut it off and connect up the right one.
In any event, this approach would simply give you the option to run other common devices, since USB-C is now pretty commonplace.
Dave