Dumuzi seems to have been taking active care to not fatally disrupt their current host’s capability to function, and deliberately left before the accumulated damage was going to be irrecoverable.
The Dead Eyes Parasite, on the other hand, actively does not care what happens to its host during its stay, let alone after it’s done with it — and even if it did, probably considers that 35-second window an entirely too large loose end as it is.
In Tim Power’s novel “The Anubis Gates”, there’s a body-jumping villain that only leaves its current host after inflicting some fatal injury or condition. Can see why that would seem prudent to such a parasite.
The Dead Eyes Parasite, on the other hand, actively does not care what happens to its host during its stay, let alone after it’s done with it — and even if it did, probably considers that 35-second window an entirely too large loose end as it is.