Good question.

I may be subject to correction but as far as I am aware, the minimum is that the bike is road worthy (i.e. has a valid MOT) and insurance.

Age of bike or rider :-) is irrelevant.
As for engine size, the bike should be able to meet National speed limits to cover all road types, so that might rule out speed limited 50cc mopeds but not necessarily as the training can be tailored to suit. However if a classic bike can only achieve a certain top speed (less than the National speed limit) but that is the bike the candidate uses, then I am sure the candidate will be allowed to use it.
With respect to indicators, if the bike passes the MOT without indicators then it is suitable for the road. Besides indicators are just one way to signal your intended direction :-)

As far as I am aware, riders and observers have used everything from twist and go scooters to custom cruisers to classic machines.

The key point of the training is to pass on knowledge gained and improve skills on how to be a better (safer) rider on the road regardless of the machine or road being ridden. So that should the rider change bikes, the skills and knowledge gained goes with the rider.

I can't back this up with statistics, but I am sure if you talk to any rider who has done advanced training, they will tell you that because of the knowledge gained they are now faster and more confident (through the bends and straights) and feel safer regardless of the size of machine they are riding.

Bb, that was a brilliant question. Got any more?