I actually went line by line through the text (using the bad Fitzgerald translation, but my Greek is not good enough to read Homer in the original except at glacial speed), leaving out the Invocation, compiling the instances in which a character makes a decision or feels a passion. Interestingly, there is no instance in which such a passion is a "stimulus" caused by a divine entity.
Agent: Priest of Apollo Passion/Action: Imploring Agamemnon to give back his daughter Motive: Unstated, but probably has something to do with not wanting his daughter to be enslaved. No divine cause
Agent: Agamemnon Passion/Action: Refuses the priest's request Motive: “it went against his desire” No divine cause
Agent: Priest of Apollo Passion/Action: Runs away from Agamemnon Motive: “the old man feared him” No divine cause
Agent: Priest of Apollo Passion/Action: Prays to Apollo for vengeance Motive: Unstated, but probably has something to do with not wanting his daughter to be enslaved. No divine cause
Agent: Achilles Passion/Action: Calls the Greeks to meet and talk about what they are going to do Motive: To figure out why Apollo is so pissed off. No divine cause
Agent: Calchas Passion/Action: Fear Motive: “I fear my man will enrage a man who has power in Argos” No divine cause
Agent: Achilles Passion/Action: Reassures Calchas that Agamemnon won't touch him Motive: To learn what Calchas knows. No divine cause
Agent: Calchas Passion/Action: Calchas explains that Agamemnon has offended Apollo by his actions (hmmmm) and says the girl should be given back Motive: To stop the plague. No divine cause
Agent: Agamemnon Passion/Action: Refuses to give back girl Motive: “Round his heart resentment welled” “I rate her higher than Clytemnestra”. No divine cause.
Agent: Agamemnon Passion/Action: Changes his mind, but requires a payoff from the army to compensate Motive: “I want the army saved and not destroyed” “It is not fitting that my girl goes elsewhere while everyone looks on” No divine cause
Agent: Achilles Passion/Action: Accuses Agamemnon of being a greedy bastard Motive: Agamemnon has everything, while the rest of the Greeks have crap for loot. No divine cause
Agent: Agamemnon Passion/Action: Tells Achilles to piss off Motive: Agamemnon's authority has been questioned; he says that if the payoff isn't good enough, he'll take somebody else's girl. No divine cause
Agent: Agamemnon Passion/Action: Orders ship with girl and sacrifices sent off Motive: To save the army. No divine cause
Agent: Achilles Passion/Action: He refuses. There is no way Agamemnon is taking his stuff Motive: “I had no quarrel with Troy” “We joined to please you so you could get revenge”. No divine cause
Agent: Agamemnon Passion/Action: Agamemnon doesn't care if Achilles deserts. “Others will honor me” However, he demands Achilles' girl Motive: “to show you who is the stronger” No divine cause
Agent: Achilles Passion/Action: Wants to kill Agamemnon Motive: “a pain like grief” No divine cause
Agent: Achilles Passion/Action: Athena talks him out of it; he'll just diss Agamemnon instead Motive: “when immortals speak, a man complies, THOUGH HIS HEART BURST” (emphasis mine) No divine cause -- Achilles acts _against his own desire_ because Athena has talked him out of it, not because of divine power
Agent: Achilles Passion/Action: Gives Agamemnon a tongue-lashing Motive: Pissed off because Agamemnon has been too much of a wimp to fight in combat, but still wants all the loot. No divine cause
Agent: Achilles Passion/Action: Refuses to fight Motive: “You will eat your heart out, raging with remorse for this dishonor done by you.” No divine cause