When you think about the word "person," what do you think it means? For us, it could refer to an individual human being whom we can see, touch, and converse. Legally, a "person" might be something that can be construed to act like one party, or it could mean someone who has "inalienable rights." So we can define a "person" as something akin to an individuated thing, something that is or is treated as a single entity.
When we deal with theological parlance, we need to extremely careful since the same word might have a different meaning from our current modern understanding. Furthermore, especially when dealing with the doctrine of God, we are dealing with the most sacred mystery and our language about God is indeed analogy. But in order for analogy to be a real analogy and not equivocity, there must be some correspondence between the word used and the actual reality. When we use the word "person" therefore as a depiction of the three in the Trinity, what are we saying? We cannot say each person is a separate single entity for example. But we also cannot say that the distinctions between the person of the Father and the person of the Son has absolutely zero correspondence to the distinction between me the author and you the reader.
So how we are to understand what a "person" means in theological parlance? We understand what a "person" means by looking at how the Father relates to the Son and to the Spirit, each of the persons to the other. So what do we see? We see the Son converse with the Father, the Son covenanting with the Father, and the Spirit working out the will of the Father and the Son. But they are all one God! So what in their actions in Scripture distinguishes them? They relate as one (the Father) to the other (the Son). In other words, they are different persons because they relate and communicate to each other differently. So how should we define "person" when we talk about the Godhead? From how Scripture portray the persons, we must say that a "person" should be defined as an individuation who relates and communicates with another.
If "an individuation of relations and communications" defines a "person" in the Godhead, then it stands to reason that each must have his own distinct will, for otherwise how can one communicate to the other? But since there is only one God and one essence, there is one will. Therefore, God has one will and three subsistent wills. And just as there is the Father, the Son and the Spirit, but one God, so there is the will of the Father, the will of the Son, the will of the Spirit, but one will.
This definition of "person" seems to me most productive, for it also works concerning the person of Christ. Since "person" is defined as an individuation of relation and communication, therefore Christ is one person, but with two wills. Christ is one person because the human will and the divine will are unified and do not contradict each other; they work in tandem. We cannot say that there is a mixed will, for a mixed will (mixture of human and divine willing) is neither human nor divine. But we can say the two wills are intertwined so tightly they function like one, and therefore Christ is one person.
It is in my opinion that the debate over the one will of God needs to deal with the issue of what a "person" is. Until those who focus on the one will of God can define a "person" in such a way that can satisfy the biblical data, I'm afraid what they are promoting sounds like modalism to me.