For the wiring, there is another approach though it might be overkill - send the video signal wirelessly between rear cam and DVR unit.
https://www.ebay.co.uk/itm/124083428240
This is from a UK seller, selected because the description includes fitting instructions, though you can get the same thing from overseas at less than half that price. I've bought one but haven't got round to trialling it yet.
One downside is that the rear cam with wireless sender will need their own 12v supply at the back of your car - rear courtesy light?
As for the rear camera, I agree these little square box cameras would look okay on a 1910s car but that was a long time ago! There are lots of separate rear view cameras sold on their own and most cams and DVTs have universal connections, so pick and choose both rather than go for these all in one packs which have this ugly rear cam (lots do!). Of course, make sure your choices are compatible with each other.
It's not easy coming up with a search term for just the cameras - all I can suggest is leave 'dvr' out of your term (e.g. 'car rear cam'); lots of dvrs will still come up, but so will the solo cameras.
lastly, for the DVR itself, once again there are a lot of cheapo offerings all gathering together around one bargain basement price, and a lot of them are the same 3 or 4 models under different brand names. I can't speak form direct DVR experience but I can from truck sat nav experience, and the cheap ones of them fall under the same cheapo brands and cheapo price point - they are generally okayish but often a bit quirky, and do not place life and limb in their hands!
If I were going for a rear view mirror version I would think about moving up one gear, and at the moment on eBay I think this means the Azdome PG12. Azdome are yet another Chinese setup, but they have a good reputation for their products beyond mere eBay feedback (which often relates more to item delivery than anything else).
One trick I have is to actually read the feedback a product has on Amazon, where reviewers sometimes actually review the product, and then see how much cheaper I can get that product elsewhere. At the moment the PG12 is about £50 on eBay and a lot more than that on Amazon! (though it does come with a slightly nicer rear cam in the Amazon listing I looked at).
Of course there are far better units than this if you want to spend more and you could spend what you car is worth on installing a DVR system, but moving up just one step from the bargain basement section has some merit I would suggest.