Unfortunately, like most sporting competitions, jousting is a test of skill, namely the skill of the two characters involved. What this means is that you can't, by definition, make the rules for this give agency to the player without taking some of that agency away from your character. These skills such as combat along with the conventional game-defined skills like Stealth are abstracted away because we, modern laypersons, generally don't know how to do any of that stuff correctly. You can certainly shoot for a more-involved lance combat system and that's fine, but I will write this post under the assumption that you won't choose that option, because it causes inconsistency in how the rules are designed (which again, isn't necessarily bad if your players are willing to handle that, just a choice).
I will try to explain with an analogy briefly in the next paragraph.
Imagine a "more detailed" combat system where you decide exactly how hard you swing your weapons. The system, besides being overbearing by many accounts, would remove some of the abstraction of rolling a die to hit. This abstraction is what "allows" your character to "make decisions" on their own, specifically the things that they are good at in place of you -- combat, for instance. In the example I'm using now, a player might say that they hit someone "with all their strength," to which the GM counters with "Haha! Now you've left yourself wide open for the enemy's attack," to which the player might ask "But aren't I an expert warrior?" By simply rolling the dice, you're leaving the "decision" up to your character, who is the "expert". Those "decisions" are luck-based with influence from your character's rated abilities, but that's just due to the limitations of the medium. You usually have a higher chance of success rolling the dice with your character's modifiers than knowing exactly what to do out-of-character.
As @Lohoris mentions, decision-making is where all the fun of the game is, unless you really like rolling dice.
With all that in mind, the approach I recommend is one where all the decision-making happens before and after the joust, not during. Maybe allow the players to choose from different lengths of lance (shorter lances being easier to aim, while longer lances allow you to roll-to-hit first perhaps), different kinds of horse, maybe the house or nation they represent during the joust will cause the crowd to cheer differently which sways the judges' opinions. However, the joust will still come down to either two rolls or an opposed check of some kind -- the details of that are mostly up to you and what accomodates the "meta-joust" rules better.
Within the joust itself, there isn't much of a decision to make, unless you're trying to decide whether or not you should kill your opponent and make it look like an accident, or whether or not you should take the fall for a bribe. Those things aren't actually involved with the game's rules, either -- they dictate one strategy, which is aim your lance at the small crest slightly below the opponent's shoulder and attempt to knock them off their horse. There is no decision there, only your skill in attempting the plan of action. Therefore the logical course of action is to avoid that part entirely and build rules around it, which is where the meta-game comes into play.
Real-life Relation / Rationale
Meta-game, despite being a bad thing in a role-playing game, is key to victory in normal sporting-type competitions. The suggestions I've provided focus on the player making decisions in the "joust meta-game," so-to-speak. They are elements that are not actually part of the competition itself, but have a substantial impact on it, whether intentionally by design or not. This layer of decision-making outside of the actual game is a good place for the player to make lots of decisions (obviously), hopefully adding depth to the game in a fun way.