The OP did not ask about culpability for dream-sinning. There is no culpability, ever. The question was, “What will is it” that we use when dreaming?
The “will” is a kind of appetite. An appetite is - roughly - a desire that can be fulfilled by the use of faculties and suppressed by other appetites. The will is the “rational appetite,” that is, the appetite which is informed by one’s reason/intellect. We have non-rational appetites - like for food, for warmth, and so on, but also for honor, for money, for love, etc. While these things only make sense with the use of the reason, we have a desire for them on account of our reason but which can act independently of it. That’s why you can have a moment of vanity without deliberating about it.
Usually, the will is supposed to be checking these appetites, moderating, suppressing, or cultivating them as is in accord with reason. (Sometimes the will has to choose a good without the corresponding appetite, like how a sick man might have to force himself to eat).
These kinds of appetites are running wild in a dream because the usefulness of the tool which the intellect and will use to moderate them (the brain) has been compromised. They are making use of the memory and imagination, both of which have been informed/shaped by our intellect but are not then being controlled by it (or by the will).
Helpful?