I can find no burial records in any Irish websites for Thomas Horton.
I assume that he was buried in or near Tralee as that was where he died. As he was English and a stranger he may have been buried in a Church of Ireland parish graveyard.
Information for Tralee regarding churches, cemeteries, and records on GENUKI Tralee pages.
https://www.genuki.org.uk/big/irl/KER/TraleeTralee was in the C. of I. diocese of Ardfert. There were Non-Conformist chapels as well as C. of I and R.C.
There are various links from the page. One is to a website about Kerry burials but the link is broken.
The bad news is that many Church of Ireland registers which had been deposited in Dublin were destroyed in an explosion and fire in 1921 during the civil war. The good news is that many survived. Collection, cataloguing, digitisation and indexing of surviving registers is ongoing.
Church of Ireland registers
https://www.ireland.anglican.org"Genealogy" tab is under "About". Information about transcription & digitisation. Links to more information.
Church of Ireland Parish Register (updated Jan. 2020)
This is a list compiled by C. of I., arranged alphabetically by parish. Entries are colour-coded. Tralee burials 1805-1873 are coded yellow which means originals survived and are in Dublin. See remarks in comment column.
Irish Genealogy.ie is the official website with civil registration records for births, marriages and deaths. It's free to use. You have to sign in each time and show you're not a bot.
https://www.irishgenealogy.ie/en/ Death registration began 1864. Too early for Thomas.
There are some church registers and more are being added. County Kerry is a work-in-progress so keep checking.
Irish Graveyards
https://www.irishgraveyards.ie/index.htmlThe accompanying map shows that the graveyards done to date are mostly in counties in 2 provinces, Connaught and Ulster. None so far in County Kerry. (Thomas may not have had a tombstone.)
Irish Genealogy Toolkit is a guide to Irish FH research
https://www.irish-genealogy-toolkit.comThere are organisations and websites for Kerry FH research. There may be some listed on the Kerry board.
I once stayed in Tralee for a few days. Was attending the Fleadh (as a spectator, not a musician). I was looking after someone's harp in a pub when another customer came up to me and asked me for a tune. The harp's owner was a stranger to me but entrusted me with her precious possession.