I'm really chuffed at the quality of advice here, and many thanks everybody.
On a couple of personal notes - no I'm not a CRI, although it's something I hope to do in the next year or so (although unlikely at On-track, simply for reasons of geography). I am a current and qualified teacher in two other areas of endeavour so not totally unaware of teaching issues, but have never (yet) been a flying instructor. I've belonged to 5 syndicates since I first bought a share in about 1997 (I think), and checkouts by non-instructors are very much the norm. Partly this is convenience & cost, and partly that many syndicates operate around aeroplanes for which a suitable instructor is very hard to find: I stay current on our old obscure aeroplanes, but few flying instructors would, or could reasonably be expected to.
But, in amongst some inevitable disagreement about whether what I (and many others) do in checking new pilots out is instruction or not, I've picked out some really useful bits of information.
It seems to come down to an approach that I should be taking along the lines of:
(1) I brief then demonstrate how to fly the aeroplane, and if required include a brief on the airfield and local area.
(2) Checkee (is that a word?) tries to fly it, with formative feedback from me.
(3) Checkee demonstrates hopefully that they can manage on their own whilst I sit there and say nothing meaningful about the flying.
(4) Either (a) welcome them to the syndicate, or (b) politely encourage them to go and get some proper instruction.
A little bit of additional flying may well be appropriate - say somebody who struggles with achieving the landing attitude, but that should be it.
Where I need to take care is undertanding that if I've got to 4(b), then I need to be clear about it. In our case, it's almost certainly going to require them to go and fly in something else, then come back for a new checkout: which is not perfect, but we don't live in a perfect world!
With regard to a pilot who won't take responsibility for their flying, despite a clear briefing that it's expected and my sitting there apparently doing nothing but enjoy the view - this clearly is a command issue that needs addressing by an FI. However, I'd still be interested to know how anybody else deals with this?
G