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If you look on the probate records website https://probatesearch.service.gov.uk/ you should find all wills and adminstrations for England for that date. My brief search revealed nothing - which would suggest that Alonzo didn't leave a Will nor enough money to need an Adminstration. It's possible that his Will was proved much later - that would need a more thorough search. If the estate had a reasonably large value it would have attracted death duties - you could try searching for that - see https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/death-duties-1796-1903/
Might also be worth a search of the London Gazette for official notices - I've had a quick search for Alonzo Goodhead and had no results, but the search engine is notoriously unreliable. See https://www.thegazette.co.uk/
If you can retrieve the newspaper article and quote it for us, we might be able to help as well.

Colour blindness I believe meant that the RN was not possible, and probably also flying duties. It wouldn't preclude army or ground-based RAF service. Mining was a reserved occupation.

Anything posted online without a link to an original record (e.g. birth cert, baptism register, whatever) is potentially suspect. Some original records are wrong (try comparing Bishop's Transcripts with the register, and compare them with other records.....). It's a minefield. And people make things up, misremember things; and the websites make what are sometimes appropriate guesses and sometimes totally mad guesses.

37 Sqn ORB is digitised, see https://discovery.nationalarchives.gov.uk/details/r/C2503026

Might be worth contacting Cranleigh. They may well know more. I can't see a direct link to an archivist, but they may well have one.