Bingo! Thank you... The problem was that I use a Matias Tactile Pro keyboard, I do not get on with the Apple keyboards, I like a full-throw key and the Alps keyswitches provide a good solid feed-back - I am twice as fast on the Matias as on the Apple keyboard.
The reversal of the function keys and the use of the 'fn' key I know about as I have it on my MBP, so I tried reversing the F-key action in the system preferences as you suggest, but using the Matias the Cmd-F would not work either way. When you suggested the FN key I grabbed the little wireless keyboard that came with the iMac and tried FN CMD F2 and it worked.
Once in five times it does not, the screen goes dark, puts a few squiggles up in the top left and sticks the cursor on the squiggles, and nothing will do anything more - until you hit FN CMD F2 again when it reverts to iMac mode. Another crack and it works fine.
Another issue I hit is that the TB cable can be inserted either way around on the back of the iMac! As it is hard to see behind the thing when inserting the cable, I got the plug the wrong way around, but it inserted just fine! Nothing worked of course. I discovered this when setting up taget disc mode, which I have used before, even with this cable, and which did work. So when it did not I started looking at the cables and noted that the little curves on the socket in the back of the iMac were on the opposite side from the TB plug (it is hard to see the polarity at the back of the iMac, it is big and close to a wall and it is hard to get a good look at the sockets). I rotated the plug 180 degrees and it went back in with the same amount of pressure as before and now target disc mode DID work. I cannot insert it incorrectly on the MBP, only on the iMac. I called AppleCare and the guy said they knew of this problem.
Thanks again.
Lawrence