The special meeting request was sent to the membership Not the board.
The general membership voted in the officer for a 1 year term. Subsequent re-election is allowed indefinitely each year.
There is nothing in the bylaws about special meetings or acceptance of resignations. When not specified in the bylaws We would revert to Robert's rules.
So the question becomes: Robert's Rules requires a vote to accept a request to be excused from duty. Who then needs to vote on the acceptance, General Membership or Board of Trustees.
Once it is accepted, it seems clear to me that the board would appoint a new officer who would take on the responsibilities of that office until the next General Election which would be in June where nominations are made for 3 weeks followed by an election.
It also seems to me that the board would need to have a special meeting to replace the officer because it is a critical position and needs to be filled right away and not wait another month.
On a side note what is the time frame for notifications for a special meeting both for Board meetings and General Meetings when not specified in the Bylaws. Is this addressed in Roberts Rules?