In jousting duels, I imagine the custom must have been to keep to the left. On TV and Movie recreations they show the riders keep to the left. It makes sense, as it allows both opponents to hold their jousting sticks w/their right hand.
Even if you were just riding down the road on horseback, it would make sense to keep to the left. You could shake hands, borrow some tobacco, saying hello to neighbors and friends you meet, using your right hand. Or defend yourself with your right hand if your horsebacked neighbor was mad at you and whacking you with a stick for trampling your horse over his newly planted corn. Anyway, it’s not difficult to imagine horse riding courtesy as being a good reason keeping to the left would become a national custom.
But when you introduce commercial scale “economy” wagons, wagons which have no driver’s seat, into a country’s landscape, it would be natural for the driver to sit on the left side horse, making it easier to use the whip from his right hand. So it would make sense for those drivers to drive on the right. And since they are the biggest thing on the road, everyone else would naturally follow suit.
That’s my theory anyway, and I’m sticking to it!