Individuals applying for military pension or military bound land warrants usually applied under a specific Act. The details of the Act indicated who qualified for a pension or a land warrant.
Most of the Acts are available online by searching for the name of the act of the date on Google or another search engine. Read the Act and remember that if your ancestor applied under that act that he (or she) must have met the qualifications. What is in those qualifications–length of service, length of marriage to soldier (for a widow), age, etc. could be clues about your ancestor.