Answer: If there are reasons for the decline, they must be shared with parents and you are the natural ambassadors for the school. In a calmer moment I'm sure your head will recognise how helpful you can be if you know the facts, quite apart from your strategic responsibility for the school's direction. At the moment he feels very raw, and I don't think you must take what he says as final. Let it ride for a week or so.
The timing needs some thought. As a minimum, you must see the analysis when it has been done and have a chance to comment. And you should see the first ideas on what enquiries need to be made, so that you can add any lines of enquiry which professionals might have missed. For the rest, I'm inclined to say let the senior staff meet on their own first. They will be in a tough frame of mind and it may pay to let them lick a few wounds before you join in.
After that, I would advocate that a small group of governors - chair and committee chairs perhaps - takes part in the discussions. The kind of issues which need to be looked at will obviously be strategic ones, appropriate to governors: the value-added calculation; differences between girls and boys; size and ability mix of groups; choice of syllabus; and any possible innovations like revision classes, practice exams in earlier years, short-term target-setting, curtailment of study leave, etc. You don't want too big a group. But later the whole governing body must be given all the information and comment which exists and a chance to add to it. There is no doubt about your responsibility for helping to put things right.
Question: Should a deputy stand as a teacher governor?
Answer: There is no restriction - but the right person can only be the one the rest of the staff elects.
If a deputy is elected, it usually means the staff feels that the individual really will represent them. If there is resistance even to a deputy being proposed, it may mean that the staff feel that the management of the school is rather hierarchical, and they therefore want to be represented by an ordinary teacher. I have seen examples of both situations many times.
Some staffrooms might fear too close a bond between the head and the deputy on the governing body to the exclusion of teacher concerns.
Many deputies never have any involvement with the governing body until they are appointed to headships - and it is very deep water to learn to swim in. But they may not even get appointed unless they can demonstrate that they know about the workings of governing bodies and have given it some thought.
Ideally deputies should have a chance to be at meetings as observers and help in preparing material for governors, as a conscious piece of in-service training. I can't say much more without knowing something about the "chemistry" of your school. Why don't you talk it over in the light of this reply with a member of staff you get on with and one who you know will be truthful with you?