Does this suggest that a large number of illnesses are purely mental? (I don't mean consciously self-inflicted). And when the mind is 'distracted' or given a reason to believe that it is 'cured' the pain stops? As with the placebo effect? ...
No - it doesn't necessarily suggest illnesses are "mental" (in the sense of "psychological", as opposed to "physiological").
The total set of Tempest63's quoted allusions plus this thread's topic consists of acupuncture, hypnotherapy, and homeopathy. These are 3 different traditions, each of which focuses on a particular context or facet of individual functions:
- homeopathy ---> physical / physiological
- acupuncture ---> neural / sensory
- hypnotherapy ---> behavioral / psychological
The boundaries among these things aren't solid, and some problems may involve a combination of some or all these aspects.
You specifically mentioned pain management. This is a good example of a problem that may involve all these functional contexts.
Pain can manifest as a result of something amiss in any of these 3 contexts, and it may require intervention in all 3 areas to alleviate it.
Unless there's a physiological / biochemical origin for pain, homeopathy is unlikely to be of any use. Conversely, if there is such a physical root cause, hypnotherapy isn't likely to help much beyond masking or hiding pain's conscious perception. Acupuncture may help alleviate the sensation of pain, but it won't directly aid you in overcoming dependency on painkillers.
Any of these approaches (as well as "scientific" medicine) can induce a placebo effect. Whether or not a beneficial outcome counts as a placebo effect depends on whether the decisive intervention affects the real cause of the malaise.