What evidence is there in "Ulysses" that the speaker does not wish for a life of adventure but instead wishes for death?

There is a fundamental tension throughout the poem between Ulysses's continuing taste for adventure and exploration, and a desire to face up to his old age and mortality. Ulysses (or Odysseus as he was known to the Greeks) was a great warrior, a noble explorer who undertook many dangerous, perilous journeys and voyages throughout the known world. It's not surprising, then, that Ulysses should still retain a strong sense of wanderlust.
But Ulysses is also mortal, so he's getting older. He's now confronted with the question of how to live out the rest of his days. Should he slip quietly into a stale, yet comfortable dotage? Or should he ignore death altogether and continue on with a life of adventure until his body finally gives up on him? As a dignified old warrior, with the blood of adventure coursing through his withered veins, there can only be one answer.
Then, what of death? I'd argue that there's no evidence in the poem to suggest that Ulysses longs for death as such. It would be more accurate to say that Ulysses seeks a new life in death, a new adventure in the afterlife, despite the fact that Ulysses is uncertain as to whether or not it even exists:

"It may be that the gulfs will wash us down: 
It may be we shall touch the Happy Isles, 
And see the great Achilles, whom we knew."

But no matter. Ulysses and his men are explorers, after all, and so there's always an element of risk involved in any voyage. Exploring the afterlife, if it does indeed exist, will be the ultimate adventure. But until the day of death finally arrives, we must all of us, brave explorers or not, in the meantime carry on our lives with vigor, purpose, and strength of will:


"One equal temper of heroic hearts, 
Made weak by time and fate, but strong in will 
To strive, to seek, to find, and not to yield."
https://www.poetryfoundation.org/poems/45392/ulysses