I can't seem to find any reason for him to be there, based on context, if I'm understanding it correctly. The painting is a depiction of the aftermath of the Battle of the Plains of Abraham during the Seven Years War between the English and the French. General Wolfe, leading the English forces, dies from multiple musket shot wounds, but successfully holds the line against the French, forcing them to retreat from Quebec. The Indigenous don't seem to take part in the battle. Was the Indigenous warrior an important figure in the war, or is he there purely as a symbol?
Here is the painting
Fred Anderson has a paragraph on this very painting in his book "Crucible of War". Anderson calls the Indian's pose "classic contemplation" and identifies him as a Mohawk warrior.
First and foremost: This painting is a romanticized fantasy version of the battle. The Mohawks were a pro-British tribe of the Iroquois, so it's not completely unthinkable that some might have been auxilieries of Wolfe's force (e.g. as scouts), but if they did they played no crucial role in the campaign. I just skimmed the chapter and the only mentions of Indians I found were of Indians fighting for the French. By right, the Mohawk should not be in this painting.
But he is.
It is hard to guess what motivates artists, but West was not a historian, he was a painter and the painting is very evocative with it's huge range of impressions. Everywhere you look, you can see different types of soldiers, officers, the news of victory, Wolfe of course ... So one of his reasons probably was to add that extra element for variety's sake.
Also, the 7-Years -War in North America was heavily influenced by Indians, mostly in favor of the French (although, again, this particular campaign was not), so his customers would expect West to pay homage to them. Furthermore, the Indian directly shows that this painting is set in America (similar to movies showing city-Skylines for no apparent reason).
The "classic contemplation" might play into the "noble savage" trope. But I do not know enough about 18th century British stereotypes on native Americans to do anything but speculate on this end.
Great question. There's an extensive art historical literature on this painting. Here's the short of it: this painting is not a realistic rendering of the men at the Battle of the Plains of Abraham. Rather, it's a "history painting," a genre of painting meant to represent timeless virtues in a classicizing style. This was one of the earliest history paintings to use contemporary history--recent events--rather than events from classical or biblical times. Nevertheless, it still portrays General Wolfe as a secular Christ embodying heroic self-sacrifice (note the compositional basis for this painting is the "descent from the cross" tradition). He was also routinely compared to a classical hero, with one officer referring to him as "the British Achilles" (see Montagna p. 81).
It also selects important figures (numerous of whom weren't even at the battle) as the "disciples" of General Wolfe. These include the Six Nations (Haudenosaunee) man (put in the traditional position of John the Evangelist, the "beloved disciple") and the man in a green coat with leggings and moccasins. Wolfe included them for a reason. After the death of Wolfe, Wolfe--arguably a mediocre figure--eclipsed in fame other men West and others saw as instrumental to British success in the New World. These included the British Indian agent to the Six Nations Sir William Johnson included by West (he's in the green coat--his name is etched in his powderhorn in one of the later copies of this painting by West) and the numerous Six Nations warriors and diplomats who were allies against the French (see Fryd p. 74). West had a history of interacting with Indians since his time as a Quaker boy growing up in Pennsylvania--he liked to tell the story he'd learned to mix paints from a Lenni Lenape man when he was a child (probably apocryphal, I think). Even though he is catering to his European audience with the "noble savage" rendering of the figure (his torso is based on the famous Belvedere torso to emphasis the "natural" beauty and vigor of the savage in nature), he also went out of his way to include precise ethnographic realism for the generic figure by using his collection of Six Nations material culture to paint the bandelier bag and tomahawk. West had complicated opinions about indigenous peoples in this painting and others, I would note.
Basically West is correcting the historical record here. He's saying, yes, Wolfe is the hero but men like Johnson and the generic Haudenosaunee man should not be forgotten for their work on behalf of the Crown.
Cited:
Fryd, Vivien Green. "Rereading the Indian in Benjamin West's "Death of General Wolfe"" American Art 9, no. 1 (1995): 73-85.
Montagna, Dennis. "Benjamin West's The Death of General Wolfe: A Nationalist Narrative." American Art Journal 13, no. 2 (1981): 72-88.
Edit: I cleaned up my writing a bit, added images, and cited pages.