You can buy the Xtrons-branded camera for about £25, or an identical generic one for about £8. I chose the latter. Actually, there are three main styles of cheap camera. One is integrated into a replacement number plate light, but my early Mk2 TT has screwed-on lamps, not the clip-in ones which came later, so that camera won't fit directly.
The other two are what you might call "square" and "bullet" types. I bought the square style, intending to attach it to the tailgate lip. Some have infra-red LEDs. Mine doesn't.
The Xtrons "manual" is pretty terse, but there's a connection diagram, plus all the wires are individually labelled (in English, plus some Chinese). The reversing camera video input is the expected yellow phono connector, but there was no description for the pink wire labelled "REVERSE", however I e-mailed Xtrons support, and they confirmed that, as I had hoped, it's an output, providing 12V to the camera when reverse is selected and the ignition is on.