Thanks again for the info folks.
Tinstaafl, yes, point taken. I suppose I was thinking of a classic jet with steam driven gauges with separate flight instruments. With EFIS and the kit behind it, presumably the EFIS either works with the AI included or it doesn't work at all, in which case the backup is an AI rather than a TC.
Indeed you don't have to have a separate TC in a light aircraft, though you do have to have a slip ball. Our light twin came to us with a single vacuum AI and an autopilot driven by it, with an electric TC. We toyed with the idea of installing a backup electric AI, but ended up with a second vacuum AI and an autopilot driven from the TC. That gives an interesting level of redundancy. Even if the vacuum system as a whole fails, at least you have
something aboard that is competent and current at partial panel.
BoxcarWilhomena, yes indeed that was what I was driving at. I would envisage that the handling characteristics of a jet (or even a high performance prop aircraft) make flying without attitude reference extremely challenging -- far more so than the equivalent loss of the AI on a light trainer.