As parlimentairan, you usually don't vote. I was one for a couple year for DECA in college and my role was to monitor the running of the meeting and to advise on motions, voting etc. If the role of this office is the true question, I would check the offical Roberts Rules of Order web site for clear answer.
If it's just a matter of your Principal wanted to be involved and know whatcha do'n
I would stop pushing them away. Yes, they are the one incharge and was hired to handle the going on's of your school.
From what I have learned over the years you have several different Principal styles-
You have the Micro Manager
The one that is everyone's friend
Mr. Relaxed
I'm sure everyone in this board could give another example, my point is you have someone that is interested and if they want to be the parlimentarian, check to see what exactly the job entails and go from there.