Side-stepping the issue of whether or not zone of truth can affect the dead entirely...
Corpses under the effect of speak with dead cannot tell a deliberate or intentional lie to begin with – in fact, they have no intent. That still doesn’t make them reliable sources of information.
The corpses just babble mostly-incoherently:
Answers are brief, cryptic, or repetitive, especially if the creature would have opposed you in life.
As the second clause indicates, the corpses of foes may have been more difficult, but even those that would have wanted to help you in life are incapable of doing so clearly. There is no thought going on; the corpse is basically just replaying some memories from life in response to questioning, and that’s all it can do.
So whatever comes out of the corpse’s mouth is inherently unreliable. It may be misleading or even inaccurate, if it’s even intelligible, even if the deceased would actively want to help you. This is not a deliberate lie, just a failing of the state that the corpse finds itself in.
Mind blank has no effect on zone of truth.
Zone of Truth (PHB, p. 289):
Until the spell ends, a creature
that enters the spell’s area for the first time on a turn
or starts its turn there must make a Charisma saving throw. On a failed save, a creature can’t speak a deliberate lie while in the radius. You know whether each creature succeeds or fails on its saving throw.
Mind Blank (PHB, p. 260):
Until the spell ends, one willing creature you touch is immune to psychic damage, any effect that would sense its emotions or read its thoughts, divination spells, and the charmed condition.
(emphases mine).
Zone of Truth isn't a divination spell (it's an enchantment) and doesn't allow the caster to sense emotions or read thoughts. Instead it magically restricts what an affected creature can say; rather than detecting lies, it just prohibits them from being spoken. The effect that lets the caster of zone of truth know whether a target has saved or not also doesn't meet any of these criteria. So, mind blank confers no benefits of any kind when being subjected to a zone of truth; a mind blanked character still needs to make a saving throw, and is subject to the effects of the spell if they fail.
Would the mind blanked creature be aware of the zone of truth?
An affected creature is aware of the spell and can thus avoid answering questions to which it would normally respond with a lie. Such a creature can be evasive in
its answers as long as it remains within the boundaries of the truth.
(Zone of Truth, PHB p. 289)
Any creature affected by zone of truth is aware of it; again, mind blank doesn't change this.
Best Answer
RAW, it doesn't say one way or the other. However, I interpret the spell as creating a zone in which not telling the truth becomes more difficult. If you fail the saving throw, you can't overcome the effects of the spell. If you succeed, however, your willpower is sufficient enough to overcome the effects of the spell. I would personally rule that a creature knows they are in a Zone of Truth after they step into the circle and either succeed on or fail their saving throw.