There is no guarantee that the majority of school teachers know what proper characteristics that ought to be found in the headmaster/headmistress of a school at the present time according to prominent scholars in Education.

A brief introduction will serve as drawing a straight line or reference points before the questions of a questionnaire are set & distributed in few schools after getting appropriate permits and seeing the teachers answering the questions without any interference. In the world of today, teachers do not like lengthy questions in a long questionnaire. So the questions have to be short, clear, and specific. Of course, the questions will not request names of participants & will not harm or defame school principals. Its purpose will be a scientific quest in order to optimize the whole process of education at schools.     

Maybe the Multifactor Leadership Questionnaire? It measures transformational, transactional and laissez-faire (passive) leadership.

We could supply you with the MyCQ, cognitive health assessment, together with a copy of my book, Executive Function - cognitive fitness for business. MyCQ uses psychometric tests to evaluate a persons cognitive health. We can help you interpret this to understand their leadership style. It's very easy to use. Please get in touch.

I will insist you make one yourself, by bring out from literature, 5 important characteristics each of the Seven(7) important and common leadership styles such as Autocratic, Distributive, Democratic,Tranformational, Transactional, laissez-faire and Situational leadership Styles. Transform each characteristic into simple and understandable questions answerable by the teachers of your sample schools. Possibly use 3-points Likert scale of Agreed, Undecided and Disagreed as your response format. As long as important characteristics of a leadership style is found ticked as agreed by the majority of teacher of a particular school, you may then  suggest that such school head is using that particular leadership style. This is predicated on a metaphysical truism which states that Universal minds is the mind of God.

Emphasis is Mine

Babalola Victor Tubosun

I disagree that teachers cannot identify the characteristics of a good administrator, however I agree that time is a factor.  You can survey teachers over their holidays for more thoughtful responses.   I would ask you if you are looking for annecdotal data or more discrete.

https://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4921&context=etd

Nice Contribution Cecilia Di Felice