Why did Legolas set sail for the Grey Havens only after Aragorn's death?

[LadyBrooke]

But even using the LotR's definition of Eldar, and not the Silm version, which would need to be clarified as to which version is used as some of use one and others the other, Legolas also proclaims himself a Silvan elf, not an Eldar. When entering Hollin, he says "the Elves of this land were of a race strange to us of the silvan folk." No matter which book is used, somewhere there is evidence that Legolas was not one of the Eldar. In Letters, Tolkien states that he is one of the Woodelves. I fail to see the evidence that Legolas is an Eldar, to contradict the clearly stated, by Legolas himself, idea the Legolas is one of the Silvan elves.

And part Eldar does not count as Eldar. For example, Finrod is part Vanyar and Teleri, so can we proclaim him to be Vanyar or Teleri in spite of it being stated he is one of the Noldor?