The important thing we have to keep in mind is which canon the boss goes to first. Once we know which canon he goes first (after resetting them) the pattern of the next once will always be the same.

"First canon" is the one closest to the lever that the boss pulls

first canon -> second, third, last, second last second canon -> last, first, second laste, middle middle canon -> last, second, second last, first Second last canon -> second, middle, first, last last canon -> middle, first, second last, second