How do I enable absence entry for an individual assignment for employees with multiple assignments?

You need to select both the Allow assignment selection at absence entry and the Allow only one assignment per absence checkboxes. You do this in the Create or Edit Absence Type page's Multiple Assignment Rules section. This ensures that all absences using that type are entered for a specific assignment.

If you don't select the Allow only one assignment per absence checkbox, you get the option to select All as an option in the Business Title field. If you select this option, the absence affects all the assignments of the employee.