I read over
Article 4 about the Office of the Mayor, and it doesn't look like there's a provision for a time when a mayor voluntarily gives up their position. It says a couple of things that might be helpful, but it looks like we're going to have to do without the Charter on this one.
Ib) No provision is made for selecting an Assistant to the Mayor, however if a current Mayor decides that an Assistant Mayor is needed to fulfil the duties of this office, he/she may propose that the Charter be amended to provide for a selection process and the standing Committee for Charter Amendments will convene according to Article 7.
An Assistant to the Mayor could fulfill the duties until Eru's term is officially over, or until she feels she can come back...but it looks as though this involves amending the Charter and I'm not sure if anyone actually wants to deal with that. I think it would be easier if we could just elect a new Mayor altogether, or assign the Mayor's duties to the Rangers.
The Mayor may have time periods when he/she cannot be on the board regularly, and may seek assistance from the Rangers by giving them advanced notice of the tasks that must be performed during that time period.
This is what we have been doing so far, I believe. It appears to be working, but if we don't get a new Mayor it might have to continue until the next election, which according to the Charter isn't until August. If the Rangers are okay with continuing to take up the duties of the Mayor, I think this is our best bet.
There's also a section at the bottom of the article that deals with removing a Mayor from office, but that's when the Mayor hasn't informed anyone on the Board that they'll be absent, and Eru certainly has informed the whole board, so that part seems pretty useless.
The only problem I see with following the rules by the Charter exactly is that the election procedure outlined in Article 4 seems to involve the current Mayor quite a bit. The current Mayor is supposed to post an announcement about the nomination period (which one of the Rangers could do quite easily it seems) but they are also supposed to head the election committee, which also involves two other posters chosen by the current Mayor.
If we wanted to hold a special election now, then I think we would have to find someone else to take over the duties of the current Mayor as far as the election committee goes. Otherwise the Rangers could continue doing the Mayor's tasks until the regular election, though that's several months away. When that time comes, Eru may or may not be willing and/or able to fulfill the duties of the current Mayor during the election, so that might just be simply putting the issue off.
So the only two options I can see now are having an election now, and waiting for the regularly scheduled election. I guess a third would to be to amend the Charter to provide for an Assistant to the Mayor, who could take over the duties of the Mayor until the end of the term, but that might be just as much of a hassle as the election.
After that overly-long analysis
...in answer to your question, TM, I don't think there's anything in the Charter that deals with this directly. We'll have to come up with another solution that's not specifically mentioned in the Charter, it looks like.