lilith says, in the opening post, that she is "interested in learning more about doing readings for people with health issues".
As has already been pointed out, the area is frought with difficulties, not the least of which is a question of timing - that ever elusive aspect in reading!
Having said this, and apart from any local judicial considerations (I have been lead to believe that in the US, readings of this nature can be mis-reconstrude easily as providing medical advice), providing readings on health issues is an area that is under-represented on Aeclectic and generally.
There are various ways and manners in which to provide such readings, and is an area that undoubtedly requires very careful, sensitive and precise communication skills. There is also a difference between making suggestions for further professional medical investigation, and diagnosis.
Even the back-trouble example is one where what may be reflected in the cards and in the context of a reading can be seen as either diagnosis, or, alternatively, an opening for further discussions that makes the querent realise that the normally accepted and unspoken complaint is something that perhaps should be paid attention to, and discussed further with one's chiropractor (or equivalent).
The example given above of someone advocating chanting or shouting for persistent thyroid problems is not something I see as a reflection of a tarot reading (and the example, in any case, suggests that a particular health professional made those suggestions following, undoubtedly, a mis-diagnosis - something ever so common in the world of medicine, and unavoidably so for most practitioners).
In the context of a reading, the throat or thyroid problem may have been seen as just that: a throat or thyroid problem that, and here, for me, is the crux, arises in the context of a reading!
Any problematic situation that specifically arises, especially if then, in conjunction with discussions with the querent, is confirmed to be in some manner problematic, warrants encouragement to seek further medical advice. If the person with the problem described above (thyroid cancer) had come for a reading with some such problems arising, I would suggest that most readers would have taken this as a sign for the querent to seek further medical advice or a second opinion to the current health advice currently followed. Personally, not only do I not see a problem with this, but rather shows one of the appropriate usage of tarot in the context of health.
With lilith's specific situation is another matter that, I would suggest, raises many of our own prejudices and our own sense of wanting to protect others: wanting to do readings with elderly people that focusses on health issues is somewhat similar to wanting to do readings with older teenagers that focusses on love - in each case, many are pre-occupied in some way or other with these respective areas of life, the difference being that the teenager is effectively less susceptible to being charged substantially (from a financial perspective).
Such potential for con-artists does not mean that those with a specific calling to such readings should not provide genuine services - on the contrary, for people with specific interests in providing such readings will in fact mitigate against the 'niche' being filled by the unsavoury type.
As to how to best read, or which deck to use, I would suggest that many decks are fine (and would of course personally recommend something like the Marseille as a good solid stock). The manner by which to deepen one's reading ability in the area of health it also to study that area: health!
Reading through even a digest health manual with one's cards, reflecting on how the symptoms or condition is reflected in the cards; reading and studying anatomy, again reflecting on how this is reflected in various cards; reading through drugs and their uses and side-effects, again reflecting on how these are reflected in the cards; becoming familiar with geriatry in general, and reflecting on various stages and its reflection in the cards; and, of course, becoming increasingly familiar (and accepting) death, the manner of dying, and the various spiritual views, and seeing on how this too is reflected in the cards - all this can lead to an increased specialised understanding that would be relevant to engaging in the specific type of reading suggested by lillith.
This does not, of course, take away from the general sense that it is an area that can be much maligned - and for good reasons. Ideally, to be sure, one's own non-tarot background would be in the health sector, and possibly include medicine or nursing... irrespective of this, the area is as open to legitimate tarot readings as is any other area of life.