though Agg AI was ticked if that makes a difference.
Not sure, since I never play that way, but I think it might. The whole point of HA rushing is to give an enemy minimal time to 'military up'. You use the speed of the horses to strike fast, preventing an opponent from building lots of archers, or worse, spearmen. Horse archers are kinda expensive for their raw power (since they are also fast), and are thus quite bad at assaulting towns with lots of defenders, from a hammer perspective.
How exactly does one go about this tactic? What is an example of a "standard" tech path and what date do you aim to get HBR researched?
Tech path first, usually you just get the necesities first: agriculture, AH, mining, bronze working, usually also pottery for a granary to enhance your wipping, roads of coarse, and hunting/fishing only if you need it. Then you beeline. I tend to skip stuff like writing or sailing. You build usually between 2-4 cities, usually 3 or 4, with decent hammers and of course also food. Then you build barracks and stables if a city is productive, never mind the stable if you can only get 3 or so HA out of it. Then you whip the hell out of those cities. 2 pops whips of course, so you wont get too unhappy a city. Get a decent amount of them, so you can quickly overwhelm a couple of major cities of your chosen target. Between 8 to 12 is usually the amount i start with, but keep reinforcements coming.
The tricky part usually isn't so much taking out an enemy, it is taking out an enemy without completely crashing your economy. You will quickly get a large empire, with few trade routes, won't always have open borders and any cottages often wont be worked due to the singing of your whip. You kind of want to quickly get Alpha and currency to recover from your early (over)expansion by military might and possibly to get some techs for a temporary peace. You also spend hammers used to build military instead of stuff for commerce (in the form of wonders like oracle, GLH or Mids, or Great person points, roads into a neighbor, etc.).
Getting that balance right is quite difficult.
On actually attacking, keep in mind that you do pay for the speed of HA. Taking on a heavily militarized opponent, or a very aggressive one that you did not choke on metal isn't really what they are for. They use their speed to attack and enemy without giving them much or any time to respond. They use their speed to threaten multiple cities at once, forcing bad decisions by an AI. Or maybe, you use them to take out a big city and their capital, and as they reinforce their other important city, take out the rest of the small ones. Trade for Alpha by then and get some techs for a peace. Then, after healing an reinforcing, take out the last strongholds. Stuff like that.