I have since put several test statments in the trigger:

Set @Indicator = (Select DependantID From Dependants Where PersonnelID = @PersonnelID)
insert into TestTable(TestColumn) values (@Indicator)

This insert is successful ever time, in every place, including at the end of the trigger. This would suggest that the DependantID is there. So why am I getting nothing at the table, and why would I get the error 'Cannot delete rows with unknown keys' when I try to delete the row without refeshing the table? (i.e. If I 'run' the table, the ID shows up fine.)