If I fix and hopefully rectify what I think might be the source of Close Votes do the voters automatically see my edits to reconsider their votes, or do they have to take the initiative?
An edit does not notify the users that have cast a vote to close, specifically.
However, if your question is closed, then the first edit to the body of the question after a closure will (usually) put the question into the reopen review-queue where it is shown in the improved form to users that can vote to reopen or vote to leave the question closed.
This may or may not include the users that voted originally.
I wrote '(usually)' as it will not happen if the question already is in the review queue for another reason (such as, a vote to reopen) or if the edit happens too long after closure (5 days). Also note the 'first.' If there already was another edit after closure before you got to fixing the question then unfortunately it will not be put into review automatically.
Reviewers will see all the "rolled up" edits at the point in time when it is being reviewed compared to when it was closed (or "put on hold").
We see a red/green view of the differences, with an alternate tab view that shows the "revised" Question as it currently stands.
Occasionally it happens that someone edits a closed Question in an attempt to improve it, but the change is rolled-back by the OP. In this case the red/green view reports that "there are no differences to display".