Thanks Graham ... I knew I was venturing into a "minefield", particularly because of the E. India Co. vs regular army question, to which I do not know the answer.
From the guide you linked me to, under "soldiers who died in service", I note "Registers of authorities to deal with the effects (possessions) of dead soldiers 1810-1822 in WO 25 ...". Probate for my fellow was 1823, so unless probate was delayed (possible for a soldier who died in India, I suppose), I'm just outside the period covered.
But one thing that the guide did not answer - as far as I could see - presumably there must have been a death certificate of some kind in order to go to probate. By whom/how would that death certificate have been issued? Would it have been an army (/E. India Co.) - issued document, or would there have been some sort of civil certificate? I can't find any!