Unfortunately the service records of soldiers who died in service were destroyed shortly after their deaths. Since widows weren't given pensions at that time, there was no need to retain the records. You may be able to find him in the muster and pay rolls for the 100th Regiment of Foot (it didn't get renumbered as the 99th until Feb 1816), but this will probably mean visiting the National Archives in person, although it might be worth checking Ancestry as they have digitised some muster rolls. However I'm guessing you have already done this as part of your general search and not come up with anything.
When searching for him more generally, it may be helpful to give the full name of the regiment, namely
100th Regiment of Foot (Prince Regent's County of Dublin Regiment) as this will eliminate the other later and earlier regiments which also bore the 100th number at various times. As the Regiment's name suggests, it mainly recruited in Ireland. Could your John Gibbons have been born in Ireland? Incidentally, it is possible that his widow might have re-married to another soldier in the same regiment. Presumably John didn't die earlier than about October 1815, assuming he was the father of Mary Ann.
The 100th Regiment have a
commemorative re-enactment society who may be able to tell you more about whether John died during fighting in Canada, although as far as I am aware the last engagement the Regiment was involved in was the
Siege of Fort Erie in 1814