altenator seems to work when it wants to no batt light comes on. on 1993 Subaru Legacy

so the car runs on the batt untill its batt light comes on so i dont know.had rebuilt ok for a while but still does can this happen without batt light coming on?checked wires ok fuses ok battery good untill it killed it.anybody know whats going on here?

Asked by for the 1993 Subaru Legacy
"seems to work when it wants to" -----HOW are you testing the charging system and are you testing it when the battery is FULLY charged?