Ok, I ended installing the reverse switch that I had ordered years ago and added to the bottom of my "Pinz - to do list" at the time.
The install is pretty straightforward, but Scott isn't lying when he writes on his technical bulletin (link higher in this thread) that the plunger that needs to be removed can be a b*tch to extract. I did not need a slide hammer like he mentions, luckily, as I don't have one, but it took a visegrip, about 40 minutes, a bit of sweat and a lot of cursing to get it out.
The joy of succeeding at the extraction was a bit curbed by the fact that when it finally gave, all of a sudden, my hand pulling on the visegrip slammed against the side of the Pinz floor...

always wear gloves...

The rest was pretty straightforward.
What would be a good pickup point for power in your view? I would like to be able to use the reverse light without the key being turned or the engine running, so my first thought (closest to the transmission switch) was to tap the power going to the radio power outlet, behind the passenger seat, which forces me to add a fuse in there, so I was wondering if there is a easy enough way to tap an already circuit-breaker-protected source that satisfies my requirements. Going under the dash is always possible, but I'll need to wire quite a bit longer, and carefully to get there accross the engine bay...