With sufficient rep you'll have more comprehensive delete vote abilities. The relevant privilege levels are "Access To Moderator Tools" for questions and "Trusted User" for answers. More info on the mechanics can be found here, but this is the relevant bit:
How a post can be deleted by a user:
Users with reputation >= 10k (more precisely, the “moderator tools”
2k on beta sites) can vote to delete questions that have been
closed/on-hold for 48 hours. It takes three votes to delete;
more if the question is popular, but ten votes at most.
Users with reputation >= 20k (more precisely, the “trusted user”
on beta sites) are not subject to the 48-hour waiting period for
deleting closed questions with a score of -3 or lower. They may also
delete answers of score -1 or lower. It takes three votes to delete
It's not easy for me to determine if a "recommend deletion" vote does not show up in you deletion votes tab or if you've just never recommended deletion on a post. Since you're an avid reviewer, I'd assume the former.