In Bramhall’s picture of human action, the will reigns supreme. No other faculty or process can necessitate (or, in Bramhall’s terms, “naturally” determine) its action. Bramhall rejects the notion that the will “does necessarily follow the last dictate of the understanding” (LN 12). He admits that the understanding does “morally” determine the will—in other words, that “the will should follow the last dictate of the understanding” (LN 12, emphasis mine). But this is a normative claim, not a descriptive one; Bramhall considers it obvious that it is possible for the will to reject the recommendations and representations of the understanding. As support for this claim, he cites Buridan’s-ass cases and cases of choosing the acknowledged lesser good (LN 46).
So Bramhall roundly rejects the claim that the understanding determines the will’s direction or action. In fact, he is careful to present the will as, broadly, in control of the understanding. He asserts that the understanding “gives no advice but when it is required by the will. And if the first consultation or deliberation be not sufficient, the will may move a review…” (LN 46). For Bramhall, it seems that the understanding’s lack of control over the will is overdetermined. As we saw above, the will can reject the dictates of the understanding. And moreover, even if the will were determined to act by the understanding, this would be a sort of indirect self-determination on the will’s part; the understanding only offers a dictate to the will when the will has requested such a dictate.
We’ve seen that Bramhall does allow for a process of communication back and forth between the will and the intellect. But it seems likely that he saw the process of deliberation as happening within the understanding alone. He defines deliberation as “an inquiry made by reason, whether this or that (definitely considered) be a good and fit means, or (indefinitely) what are good and fit means to be chosen for attaining some wished end” (LN 59). Here’s one possible story about how this search-for-means could work in the context Bramhall’s psychological picture: the will sets ends for the understanding by prompting it to consider how to accomplish a given end. It is the understanding’s role to find an adequate means to that end. The process of thinking through these means constitutes deliberation (recall that “deliberation is of the means, not of the ends” (LN 64)). Once the understanding proposes a certain means as a course of action to the will, the will can still reject that means, thereby triggering further deliberation within the understanding.
 It’s possible that Bramhall might want to define deliberation more broadly, as some subset of the communicative process between the will and the understanding. This subset would have to exclude the process of setting ends; after all, deliberation is of means, not ends. But there might be some other role for willing within deliberation: consider, for instance, a willing to search one’s memory for possible solutions to an already-set problem. I see no particular evidence that Bramhall endorses a definition for deliberation like this one, but it is certainly a possibility open to him.