Yes there are working Mac Mini 2012 eGPU setups.
My old GTX 570 (with your EFI) as eGPU works on my MacBook Pro 13' 2012, but not on my Mac Mini 2012. The Mac Mini crashes at startup.
I think it could be an issue with the GTX 570. So i ordered a PC GTX 770 to test as eGPU, but I'm still waiting for the card.
Some time ago i did the EFI firmware update 1.7:
http://support.apple.com/kb/DL1616
I hope i did not broke the ability for eGPU with the update
The confusing thing here is the term "EFI"
Apple used one of their making on 2006/7 Mac Pros.
Then a new 64bit one on 2008 MP. As we have recently discovered there is in fact a 3rd version on 2009-12 MPs.
So the GTX570 you got from us would have one that works on 2008 MP and 2009-12 MP. Apple has since switched to a different one.
They could have easily used the UEFI standard like everyone else but that would have made everything too easy. (and allowed 3rd parties to sell upgrades like eGPUs)
They have once again created a new EFI that doesn't adhere to previous EFIs form them, or the industry standard one. We have gotten a loose idea of how this new one works and have it functioning on some cards.
Fairly sure I could do one that would enable the 570 on your Mini but then it would likely not work on MP anymore.
EFI was supposed to unify things, instead Apple found another way to fragment markets and keep their stuff "special". I may someday be able to combine a cMP EFI with a nMac EFI and retrofit my old cards, but that will likely require new EEPROM chips to hold all of the files. Meanwhile trying to finish Mac Edition 970/980 cards and ship them. Oh yeah, and the rest of my life too.
So much stuff could be done, but so little time.
In a perfect world I would have a giant facility here in Hollywood where there would be 1 of every Mac ever to have a PCI/AGP/PCIE slot. I would have a team of trained buyers getting all of the right used cards on Fleabay and CL. Steady handed guys or girls would solder on the new chips and flash and test the cards. Bad leaky caps would be replaced, dust cleared, fans replaced.
Would be a 1 stop shop for every Mac that could take a video card. We did the first Core image cards for Cube (6200 WANG XFX), the fastest cards for PPC (7800GTX512 and 7800GS) and basically EVERYTHING for Intel MP. Along the way had help from Arti Itra, Thomas Perrier, and Netkas. Anyone have an unused factory in Hollywood?
The eGPU thing is even more exciting and would ideally require 1 of each TB Mac ever made for testing. A variety of displays, especially new 4K and 5K and HDMI 2.0. The TB eGPU thing is really exciting, but have not had time to push it forward. Still planning to get something out to Barefeats so the incredible possibilities get more widely known.
Here is an example of something that needs refinement. I have found a way for a 2014 Mini to have 100% reliable boot after boot after boot eGPU. But it requires 2 GTX780s. Using just one gives a 60% reliable boot screens while adding 2nd one makes it perfect. But then you have twice as much in eGPU as you do in Mini $$$$-wise. Just another detail to figure out.
I will say this, the 3 different TB2 machines I have tested have been pretty similar in their behavior. SO what has worked on Mini 2014 has worked on nMP, etc. My 2012 rMBP is MUCH easier to deal with, doesn't require the eGPU EFI and can run a bunch of displays. TB2 stuff much more limited. 2012 Mini shouldn't be too difficult. If you are in LA area drop it off and I can make it work.