Why would it matter? Here is one reason.
If the experts are evenly divided on some question, many will urge that that the rational thing to do is to suspend belief. To satisfy the dictates of reason, then, one ought to suspend or withhold belief in some cases. But 'ought' implies 'can.' So, if one ought to suspend belief, then one has the ability to suspend belief, which implies that at least some beliefs or rather believings are under a person's voluntary control. I say that some are. That makes me a limited doxastic voluntarist. Catherine Elgin says that none are:
Belief is not voluntary. Belief aims at truth in the sense that a belief is defective if its content is not true. If believing were something we could do or refrain from doing at will, the connection to truth would be severed. If Jack could believe that Neanderthals were an evolutionary dead end just because he wanted to, then his believing that Neanderthals were a evolutionary dead end would not amount to his thinking that 'Neanderthals were an evolutionary dead end' is true. For nothing about the fate of the Neanderthals is affected by what he wants. ("Persistent Disagreement" in Disagreement, eds. Feldman and Warfield, Oxford UP 2013, p. 60)
This argument leaks like a sieve. Either that, or I don't understand it.
It is true that belief is connected to truth. But what exactly is the connection? If I believe that p, then I believe it to be true that p. That is the connection. I cannot believe that p without believing that it is true that p. But of course my believing that it is true that p is consistent with p's being false.
Now suppose that the evidence available to me for and against the existence of God is equal, and I choose to believe for prudential reasons, say, or for no reason at all, that God exists. This choosing to believe would not sever the connection between believing and truth. For again, the connection is just this: my believing that p entails my believing that p is true. That connection remain in place whether or not believing is voluntary. My believing that God exists does not make it true that God exists. Believing entails believing to be true; it does not entail being true!
The same holds if I choose to disbelieve that God exists or if I choose to suspend belief. My disbeleiving that p does not make p false. And my suspending that p does not make p indeterminate in truth value.
Elgin tells us that "a belief is defective if its content is not true." But surely an occurrent mental state is a believing whether or not its content is true. A false belief is just as much a belief as a true belief. Surely Elgin is not telling us that only true beliefs are beliefs! But then what is she saying?
Elgin writes, "If Jack could believe that Neanderthals were an evolutionary dead end just because he wanted to, then his believing that Neanderthals were an evolutionary dead end would not amount to his thinking that 'Neanderthals were an evolutionary dead end' is true."
Elgin seems to have a 'straw man' conception of doxastic voluntarism. After all, no one holds that the fate of the Neanderthals depends on what anyone thinks or believes. If the paleontologists are evenly divided on the question and Jack chooses to believe that the Neanderthals were an evolutionary dead end, he is not thereby committing himself to the absurd notion that his so believing makes it true that the Neanderthals were an evolutionary dead end.
With respect to a purely theoretical question like this, one the answer to which has no practical consequences for the believer, the doxastically (as opposed to practically) rational thing to do would be to suspend judgment/belief. If so, then some believings/disbelievings/suspensions come under the control of the will.