Hello. So as all things related to the inner-workings of the Spartan Politeia, we do not have a complete understanding and must make assumptions based on piecing together the evidence that is available. Thankfully because the Kings were some of the most visible figures outside of Sparta we do have a few actual instances of Spartan Kings’ decision-making that we can use as case-studies. Since you asked about primary sources (as all ancient historians should!) we’ll focus on some of these and explore how the kings interacted with each-other and how their power changed over time. I will focus on the fifth century BC.

Perhaps the most obvious example of the kings making divergent decisions, and the consequences of this, come from the conflicts between the Kings Cleomenes and Demaratus. In 508 BC Cleomenes had supported an oligarchic government against the fledgling democracy in Athens, but had been expelled by force. He mustered the Peloponnesian forces for war against Athens: at this time both Kings exercised equal authority as the supreme commanders over the Spartan military. However when the army mustered, some of the Peloponnesian forces did not support the campaign, and eventually Demaratus departed with the Spartan forces too - at direct variance to Cleomenes. Herodotus explains (5.72-6) that this conflict between the two kings gave rise to a new law in Sparta, whereby when the Spartan army was dispatched, only one King would command it whilst the other remained in Sparta.

Herodotus’ account seems to indicate that the Kings had a very direct and authoritative sway over foreign policy decisions in Sparta in the early fifth century. Indeed later in his account he claims (6.56-60) that the Kings had “the right of making war against whatsoever land they please, and they no man of the Spartans shall hinder this right, or if he do, he shall be subject to a curse”. It is hard to corroborate Herodotus’ account here, since our other extant accounts on Sparta focus on the later fifth century and later. But based on other events from his narrative it does seem like the Kings did have a big role in foreign policy decisions. For example when Aegina accepted Persian demands for earth and water, in the 490s BC, Cleomenes attempted to arrest members of the Aeginetan government, but he was rebuked because “he had no authority from the Spartans for what he was doing... otherwise he would have come to make arrests with the other king” (6.50). If we read between the lines of these examples, perhaps what Herodotus is capturing is a growing constitutional struggle between the two kings who were trying to exercise their authority over foreign policy, and that intervention from other governmental bodies within Sparta were beginning to redefine the Kings’ power as a result. This can be later seen when Demaratus is exiled because, at least according to Herodotus, Cleomenes questioned Demaratus’ birth legitimacy and bribed the oracle of Delphi to support his accusations (read more about that Herodotus 6.60-69).

Accusations of kings accepting bribes, attempting to set up tyrannies, working with the Persians, and stirring Helot revolts, plagued the Kings in the early 5th century. See further Cleomenes (Herodotus, 6.74-5) Leotychidas (Herodotus, 6.72), the regent Pausanias (Thucydides, 1.130-135), Pleistoanax (Thucydides 5.16). I would argue this reflects the nature of the King’s power and how (if we believe Herodotus’ claim about the Kings’ unquestionable authority in war) the Spartans were beginning to question their unchecked decision making capabilities. It must be noted that in all of those circumstances the kings were held to account, usually by the Ephors.

When we contrast this with kings in the later fifth century, we see far more direct oversight over the Kings’ abilities to make decisions. Domestically they were permanent members of the Gerousia, but even Herodotus claims their domestic duties were largely ceremonial or religious as opposed to political. But with regards to legislative decisions their influence was diluted by the other members of the council. When it comes to foreign policies at some time in the 5th century it appears the constitutional authority of the Kings was changed. Both Aristotle and Xenophon tell us that two Ephors would accompany the King on campaign, making note of his conduct and having the power to prosecute them for malfeasance in the event that their decisions contradicted the wishes of the state. This happened for example with King Agis in 418 BC when he made peace with the Argives contrary to the wishes of the government, Thucydides (5.63) says the government threatened to fine Agis ten thousand drachmas, and instituted a new law for 10 counsellors to oversee Agis’ decisions and who’s consent he needed to lead an army out of Sparta.

Indeed, their power to exercise full authority over war also appears to have been stripped by the Peloponnesian War. In 432 BC when the Peloponnesian league met to discuss the issue of war with Athens, Thucydides tells us that the final say did not lie with the Kings, but instead the Ephors “put the question to the assembly of the Lacedaemonians”, who first voted via acclamations and then by separating into two groups when the vote was too close to decide (1.87). This is significant because it directly went against the wishes of the King Archidamus, who had expressly advocated delaying any open conflict with Athens at the meeting. Clearly the decision no longer rested with the Kings.

So as you can see the question of how decisions were agreed upon and made between the two Kings actually became a constitutional issue in the early half of the fifth century BC, and that over time - at least if the contemporary sources are giving us a somewhat accurate picture - that power was slowly diluted as oversight of the King’s decisions were handed to the Ephors and their say in domestic and foreign policy issues were shared among the other institutions of Spartan government.

Hope this helps!