The break in service if considered as dies non then that period may not be included for the total length of service, however the service rendered shall be minus this dies non period.
In any case you are eligible for gratuity for the total length of service minus the dies non - period, however you may refer to the leave regulations that the study leave whether with or without pay can be excluded from the length of service, it should not be excluded, if it is recognised as leave then you are eligible for gratuity for this period too.
The rule for the Payment of Gratuity Act 1972, you mentioned is correct. One should have completed 4 years and 240 days (8 months approx) to become eligible for Gratuity.
In section 2A (Sub section 2) it is mentioned that (2) where an employee (not being an employee employed in a seasonal establishment) is not in continuous service within the meaning of clause (1), for any period of one year or six months, he shall be deemed to be in continuous service under the employer -
(a) for the said period of one year, if the employee during the period of twelve calendar months preceding the date with reference to which calculation is to be made, has actually worked under the employer for not less than - i) one hundred and ninety days, in the case of an employee employed below the ground in a mine or in an establishment which works for less than six days in a week and (ii) two hundred and forty days, in any other case;
IF his resignation is accepted then D.o.J. to Resigned date to calculate gratuity and if not, then D.o.J. to when employee will resigns and those days when he was on personal work will also be part of continues service because those days were permitted in written by authorised person/company