What if the individual wishes to avoid the rebirth of their soul either to extend their current "life", out of obligation to their people, to atone for the sins of their life through service, or out of pure terror of what judgement might befall their soul (heck, giving a monstrous psychopath the voluntary opportunity to at least temporarily avoid bad-afterlife (i.e. hell) in exchange for service as a mindless skeleton might be more mercy than they deserve). Is it known what a soul experiences when their body is animated as a mindless undead?
Most individuals who choose to become undead would do so for one of the reasons you've described. Are you asking me what, say, a Priest of Ammonar would say to someone who claimed those motives?
Mindless undead (being mindless) are mostly animated by tainted power that was immanent within the environment. As such it's the most innocuous form of undeath. It's not entirely innocuous however. When a person dies, some of their soul (which is itself a shard of the Logos) remains as residue in the body. This is why the Empyrean faith cremates the dead (to allow everything to pass on). The residue of the soul in the body is also what you're speaking to when you use Speak With Dead, and it's what you are tapping when you use a monster part as a special component.
Also, is this "taint on the Logos" a philosophical issue, or capable of measurable harm on the world (much like how sinkholes of evil arise in places of death, do high concentrations of undead create dangerous situations?)
We're getting pretty deep into metaphysics of the Auran Empire here, but the Logos is immanent within everything. I explain it in the Auran Empire “esoteric cosmology” as follows:
“everything in the Cosmos has a trace of the Logos within it, and living things have a veritable shard of the Logos in them. This shard is called the soul, and carries a measure of divine power. “
A sinkhole of evil results when the Logos immanent within an area is tainted. When a body dies within a sinkhole of evil, the taint can seep in, which is why mindless undead rise from dead bodies in sinkholes of evil.
Do undead and sinkholes of evil create measurable harm on the world? The Empyrean gods teach that the transmigration of the soul is not just right, but necessary for the functioning of the world.
The Chthonic gods teach that the transmigration of the soul is a lie, and that the Empyrean gods actually eat your soul. After all, if you are “reincarnated” why don’t you remember your past lives? Chthonic gods (so they claim) are the only truthful gods, because they tell their followers how to become undead and preserve their ego-self.
Again, from the Auran Empire campaign setting:
“The Empyreans believe that after death, the body must be burned so that the spirit can swiftly travel to the afterlife, where its valor is weighed by Türas. Noble souls might pass to the Empyrean Heaven and dwell in the light. But most souls drink of the waters of sorrow and return again to the realms of man in a new body.
“Chthonic faithful do not believe in this cycle of life, death and rebirth. They believe that upon death, the Empyrean gods consume the soul, and then use it as fuel in the creation of new life. They see reincarnation of the soul the same way we see fungus growing in a corpse – new life, yes, but not the same life. They see, not a choice between undeath and reincarnation, but undeath and oblivion. They thus seek to keep their souls and their bodies intact until the time of the Awakening, lest their singular identity be destroyed by the cycle of death.”
“The Chthonic religions all seem to prophesize a time known as the Awakening, when the gods shall return to the earth and the faithful shall enjoy bodily resurrection. The day of this Awakening is said to be governed by the movements of the stars, which are eternal and unchanging, their truth hidden by the false light of Ammonar’s sun.
Lastly, what happens when a caster controlling many mindless undead dies? Do they follow their last order until destroyed (making their danger based on just what that last order was) or do they suddenly (or at least eventually) break free and start killing people? What happens when the mage is brought back, or "dies" only to immediately rise as a lich at the end of a successful necromancy attempt?
The undead continue to carry out whatever their last order was. A mage who is brought back still has whatever control he had over them.