A: As to the first part of your question, I do not see why not in principle as it is an allowance. The essential question is whether it can be shown that you are doing the whole job. Who would cover the responsibilities while you were not working? If you were leading a department where the subjects were only taught on days you worked, you might feel you could do the job. But, what if essential meetings were held on days when you were not working? Who would represent the department?
The school shouldn't pay you pro rata and not pay anyone else to do the remainder of the week. So, a job share is fine, but paying you part of the TLR for your part-time hours would not be so, in my opinion, and the school would need to explain how the job is covered during the period for which you are not being paid
As to a "glass ceiling" for part-timers, the profile of the profession is changing and work-life balance issues are more important so schools may be more flexible. It is less than a decade since co-headships were first recognised. In the end it is a matter of supply and demand. If there are sufficient full-timers, why should schools consider part-timers?
John Howson is a recruitment analyst and visiting professor of education at Oxford Brookes University. To ask him a question, email him at firstname.lastname@example.org.