The famous Conestoga covered wagon is to blame. Named for their place of manufacture - Conestoga, Pennsylvania.
Despite popular belief, these were not the wagons used by pioneers during the westward expansion – much lighter, standard farming wagons were used. The Conestoga wagons were huge, heavy duty constructions designed to haul heavy goods. Think of them as the semi-trailers of the 18th & 19th century.
On Conestoga wagons the handbrake lever was on the left, so drivers sat on that side, centering the wagon on the often heavily cambered, mostly unpaved roads. Even with a huge team of horses or bullocks, average speed was walking pace, so drivers often walked alongside, or rode on a pull-out board known as a lazyboard. So whether standing, walking or sitting - the left mounted handbrake had to be accessible.
The Conestoga wagons were so popular it soon became the standard to sit at the left and drive on the right. So when automobiles came on the scene - they simply followed existing practice.
The town of Conestoga has one other claim to fame - according to author Bill Bryson it's where a popular brand of cheap cigar was made that became known as Stogies (short for Conestoga of course…)