You are right about the name but just between you and me the plains were a long way away and the redoubt was on the top of a hill with good sight-lines etc., all of which would make sense 'cos you sure want to see the enemy coming before they arrive. But the ships bombarded the fort prior to the attack anyway ....
My whole point though in posting anything was my surprise that this lad was at the Grammar school in Inverness at all. In fact , based on his history ( he was the aide de camp of one of the generals who served Cumberland at Culloden), after the skirmish was over, he would certainly have accompanied the other officers and most of the army who descended to bivouac in the town. He must have been quite young though and if he attended the school to learn it could have been a University-type course I would have imagined.
Isn't it much more likely, though, Charles, that he was simply staying there between shifts. I will bet that the available accommodation for all the army would have been very scarce and the school probably offered more space for the upper crust types not to mention tables and chairs for conferences etc.