Only 'on health grounds' works.

Student or Learner
Are "on health grounds" and "on health conditions" interchageable here?
Ngram shows that both were active at the same level in 1940s and then the latter began to decline in use.
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Sir Ernest Henry Shackleton CVO OBE FRGS FRSGS was an Irish Antarctic explorer who led three British expeditions to the Antarctic. He was one of the principal figures of the period known as the Heroic Age of Antarctic Exploration. Shackleton's first experience of the polar regions was as third officer on Captain Robert Falcon Scott's Discovery expedition of 1901–1904, from which he was sent home early on health grounds, after he and his companions Scott and Edward Adrian Wilson set a new southern record by marching to latitude 82°S.
Source: Ernest Shackleton - Wikipedia
Only 'on health grounds' works.
Typoman - writer of rongs
Would "on health reasons" work?
No.
Typoman - writer of rongs
You can use:
- on health grounds
- for health reasons
- because of/due to a health condition
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.