Better late than never...
His out-Pension would have been available to pick up in person once every 3 months. Anyone attempting perpetrating "benefit fraud" would be in trouble, as impersonating a Greenwich or a Chelsea out-Pensioner was punishable by death! I would have thought that some kind of docket was issued when a pension was granted, and thereafter the clerk would know the out-Pensioner.
Whilst better than nothing, the out-Pensioner would have had a "day job" of some description, quite often being an agricultural labourer. Given that marines were recruited away from port cities, with The Enclosure Act and the automation of the textile industry being the "push" that made men join the marines, they will have tried to go back to whatever profession they had held prior to enlistment. The out-Pensioner and former marine John Milham appears as an agricultural labour on the census, I recall.
The out-Pensioner would attend a Pay Office to collect said pension. Several Pay Offices would be in a Pay District. I am guessing that either Newcastle or Durham would be the Pay District under which your man's Pay Office related to. Here is a partially completed listing.
https://webarchive.nationalarchives.gov.uk/ukgwa/20130221213556/http://yourarchives.nationalarchives.gov.uk/index.php?title=WO_22I got the impression that the logistics of communicating the Naval General Service Medal & the Military General Service Medal to the masses, that had survived, was facilitated by these Pay Offices. The out-Pensioner would have been able to make an application via the Pay Office. Any medals to be issued could be done so via the Pay Office, in the same manner that their quarterly payment was done in a secure manner.
The clerks of the Pay Districts would undertake "variance analysis" reporting. This would document newly admitted out-Pensioners, and those who had died, for whom no further out-Pension payments would be forthcoming. Those that have survived have been collated in the WO 22 series of archival records. FindMyPast digitised these records in 2016, if I remember rightly.
Whilst army service does seem to have had the pension as a deferred remuneration, I got the impression from Bruno Pappalardo's book on navy records, and Matthew Little's book on Royal Marine genealogy, that navy pensions were for the "deserving poor" who were "worn out" or injured only.
It is a shame that the Napoleonic Wars forum is no more. There is the following alternative, but it has more land-based content:
https://www.thenapoleonicwars.net/forumCheers
GP