I wonder:

if you had an agent that obviously did have goals (let's say, a player in a game, whose goal is to win, and who plays the optimal strategy) could you deduce those goals from behavior alone?

Let's say you're studying the game of Connect Four, but you have no idea what constitutes "winning" or "losing." You watch enough games that you can map out a game tree. In state X of the world, a player chooses option A over other possible options, and so on. From that game tree, can you deduce that the goal of the game was to get four pieces in a row?

I don't know the answer to this question. But it seems important. If it's possible to identify, given a set of behaviors, what goal they're aimed at, then we can test behaviors (human, animal, algorithmic) for hidden goals. If it's not possible, that's very important as well; because that means that even in a simple game, where we know by construction that the players are "rational" goal-maximizing agents, we can't detect what their goals are from their behavior.

That would mean that behaviors that "seem" goal-less, programs that have no line of code representing a goal, may in fact be behaving in a way that corresponds to maximizing the likelihood of some event; we just can't deduce what that "goal" is. In other words, it's not as simple as saying "That program doesn't have a line of code representing a goal." Its behavior may encode a goal indirectly. Detecting such goals seems like a problem we would really want to solve.