I can’t tell from your post whether or not the strata manager has delegated powers to act on behalf of the committee.  

If they do, then they should have organised an AGM.  

Your message is quite confusing as you say there is no executive but that there is one member.  It’s either one thing or the other.

I’m not sure that you legally need an EGM to fill vacancies on a committee unless the membership of the committee is now less that the quorum (half the number of committee members agreed at the last AGM). If that is the case, the committee has ceased to function and an AGM or EGM should be called to hold a new election.

If you have asked for a meeting for this purpose and the remaining member has failed to organise one within two months of your request (in writing), you can apply for section 232 orders at NCAT requiring a meeting to be held.

If the remaining member is not prepared to act as the chairman or secretary of the strata scheme, you can apply under section 48 of the Act (see below) for the Tribunal (NCAT) to appoint someone (probably you) to act as secretary and chair and organise a new election.

It may be that the strata management contract allows the strata manager to assume the duties of the committee in the case of a situation like this. 

If so, you might cut some corners and tell the strata manager that if they don’t organise an AGM immediately (because you can now hold your AGM at any time in the financial year) you will report them to Fair Trading and thereafter closely examine the terms of their contract to see if it should be renewed when it comes up, as it legally must, some time in the next year.

I have to say that it is not unusual for strata managers to be lax when it comes to small schemes as there is comparatively little revenue for not much less work.  It may also be that that the strata manager and absentee owner have a cosy “no hassles” relationship that suits both parties to the detriment of the strata scheme.

Nothing will happen before the new year for the reasons you have stated but the first week in January you need to be writing to or calling the strata manager and telling them that their reputation and future contracts are on the line.

So get a hold of the strata management contract and establish whether or not they are acting in lieu of a functioning committee.

You also need to get the support of two of your neighbours before the election to make sure you can restore some sense to the whole business.

And, just to be clear, the Owners Corp has to pay for repairs of common property, regardless of who is on the committee and whether or not they want to. 

48 Tribunal may order meeting if no officers or strata committee
(1) The Tribunal may, on application by an owner, mortgagee or covenant chargee of a lot in a strata scheme, make an order appointing a person to convene and hold a meeting of the owners corporation if there is not a chairperson, secretary and treasurer of the owners corporation, or if no strata committee exists, after the first annual general meeting of the owners corporation has been held.
(2) The Tribunal may make any other ancillary orders it thinks fit, including the following orders:
(a) orders relating to giving notice of the meeting,
(b) orders relating to the person who is to preside at the meeting.
(3) The person who is to convene and hold the meeting is to be a person nominated by the applicant, or appointed by the Tribunal, who has consented to the nomination or appointment.
(4) The meeting is to be convened and held within the time (if any) specified in the order.
(5) A person appointed by an order under this section to preside at a meeting is taken, while so presiding, to be the chairperson of the owners corporation.