Hi Glen,
One 'obtrusive' option would be to use a vintage back up light and hang it off the quick jack like you did for the driving lights on the front. Not sure if you can get by with one, or if you need two.
They also have rear fog lamps as well, but that is even more 'obtrusive' ; )
My guess is you don't get much fog in your area and if it was foggy, you would probably not be driving around. This company is in the UK, but I am sure you can find something similar closer to home.
https://www.s-v-c.co.uk/category/fog---reverse-lights/
- Tim