In the Introduction to The Scarlet Letter, "The Custom-House," in what war did General Miller fight?

In Nathaniel Hawthorne's novel The Scarlet
Letter, the General is a minor character who appears in the Introduction
called "The Custom House." This Introduction, originally written by Hawthorne as an
independent and unrelated short story, sets the frame from which the story of Hester
Prynne, Pearl and Reverend Dimmesdale is told. General
Miller is the head customs collector at Salem Custom House, a government
installation for collecting customs duties on items coming into America through the
Salem seaport. He enters the story because the narrator of "The Custom House," who is
presumed to be Nathaniel Hawthorne himself speaking as the narrator, takes a position at
there and thus meets that General and the other colorful employees, who all shave either
inherited their rather low-key work positions in customs or been awarded their positions
as retirement rewards for other services rendered to the
government.

Typical of this trend, General
Miller was awarded his position for his service in and record as a war
hero of the War of 1812. At the time that the narrator
meets him, he has served twenty years at the Salem Custom
House:

[T]he
Collector, our gallant old General, who, after his brilliant military service,
subsequently to which he had ruled over a wild Western territory, had come hither,
twenty years before, to spend the decline of his varied and honourable
life.

This Introduction is
relevant to the story of The Scarlet Letter because it is at the
Custom House, or "Custom-House" as the Introduction puts it, that the narrator finds the
package that tells the story of Hester Prynne. The General is important to the story
because it can be argued that Hawthorne uses him to foreshadow both the great weight
that an error can have on a conscience imbued with keen integrity and the ability of
some, like Hester and Pearl, to survive great
plights:

His
integrity was perfect; it was a law of nature with him, rather than a choice or a
principle; .... A stain on his conscience, ... would trouble such a man ... though to a
far greater degree ... I had met with a person thoroughly adapted to the situation which
he held.