I have a copy of a little publication by Glasgow & West of Scotland FHS from 1986 entitled Burial Grounds in Glasgow - A Brief Guide for Genealogists. There is no mention of St Enoch's Church or any churchyard/burial ground attached to it.
Presuming that the said church was somewhere in the vicinity of the current St Enoch Square, the nearest burial grounds were -
Blackfriars Churchyard (or College Churchyard) High Street, this was an ancient burial ground, demolished 1875. Registers for 1776 - 1854 should be at the Mitchell Library. Mitchell may also have some MIs.
The town hospital in Dunlop Street, closed before 1831, demolished before 1858. So theoretically it could still have been open for interments in 1825. No known burial register for that period and no monumental inscriptions list.
Ramshorn, St David's - you have already searched.
High Church/Cathedral/Old Barony Church, Cathedral Square. an ancient burial ground, new burial ground opened 1801, crypt in Old Barony Church opened about 1805 closed 1835. Mitchell Library should have burial records and some MIs.
Anderston Old Churchyard at Heddle Place and St Mark's Anderston at Cheapside Street were both, as far as I know, secessionist churches. So if Dr Taylor is listed in the Fasti he wouldn't have been buried in either of these.
There was another burial ground in North Street, presumably Church of Scotland, first burial there was 1821. Burial records only begin at 1830, there may be a few MIs but I think they will still be in unpublished manuscript form at the National Archives in Edinburgh. (Or whatever they are calling it nowadays).
Glasgow Necropolis didn't open until 1832.
Sighthill Cemetery opened 1840.
Southern Necropolis (Gorbals) opened 1840.
Good luck with your search.
