You are eligible for Gratuity, there is a notification from Central Govt in respect of amendment in definition of Employees under the Act and after that it is applicable to all kind of employees who employed in any kind of shop & Establishment. it was extended to educational institute in year 1997 by notification.
Notification regarding change in the definition of employee came on dated 31.12.2009. Judgements are of earlier dates. After this notification we have not seen any such judgement which disallow gratuity payment to teachers. The Payment of Gratuity Act, 1972 applies to every shop or establishment within the meaning of any law for the time being in force in relation to shops and establishments in a State in which ten or more persons are employed or were employed, on any day of the preceding twelve months and thus if this private school is covered under this Act then in my opinion teacher will definitely get gratuity under this Act.In your case the law enforcing agency is the State Labor Department & therefore first approach them & let us know what they say for further discussion/ comments.