I have never seen all red mk3 lights per say BUT I know what you mean. My 94 has the amber top turn sections and I really dont like them. I ordered a set of clear lens for it and then used Night-Shade red tint spray to turn them red.

You have to put a few coats and they get darker and darker with each. They came out great!

This is a bit of an educated guess, but I think the reason all-red tail lights are so scarce is that they only used them on US spec cars. So that would mean that Minis made after 67 never had them as an option. My Elf uses the same tail lights as an Austin 1100/America, and when I found my red ones, the Lucas packing had the same part numbers as the red/amber ones, the lenses are made with the exact same mold numbers, but the box was stamped EXPORT. 

I was able to find some MK 1 red uppers but no such luck with the MK2 on rears. I'm still looking and my local buddy who has 6000 sq ft of NOS Lucas is looking for me as well. He has spent countless hours adding all his part numbers to his computer. If you have a part number Lucas or Rover/ BL /BMC I'll be glad to have him check. Steve (CTR)

Seen a few minis which seemed to be mk3 cars with all red tail lights rather then the multi color..

Anyone know who carrys them? Or is it a mismatch of different style lenses? Thanks