Because I know so little of the naval forces in the Crimea, I asked an expert and attach his reply. I was a bit nonplussed about someone from the navy being in the Battle of the Alma (a land battle), but an explantion follows:
Captain Keppel , not Kepler, of course.If he came to Black Sea with Keppel he couldn't have been there at the time of Alma, so was possibly transferred later.Not unusual for RN personel to describe their trip ashore to collect wounded after Alma as 'being at Alma'.As for records, most of the musters for the ships are extant at the NA - PRO Kew. Plus medal rolls. Plus service records.I have the muster and medal rolls for the naval brigade ashore and there are several John Martin, but no John Patrick Martin, but he might be one of them.Trip to Kew, or employ professional researcher there, only way forward.Sounds to me as if he jumped ship in Sydney - captains hated visiting there because they always lost so many men (during gold rushes especially).
Not very encouraging, but adds a bit to your knowledge and suggests a course of action if you want to pursue the research.
Lawrence W. Crider Author, In Search of the Light Brigade Editor, The War Correspondent: journal of the Crimean War Research Society