I don't recall any significant difference in afterburner light times at altitude vs. sea level on the J-79s. Some had a modification so that the burner torch had to be lit each time (for night invisibility reasons). If the AB igniter got coked, you still could light off pretty promptly just off turbine torching. The J-79 had an excellent 4 stage burner that modulated nicely, not at all like the J-57s which were either on or off.
But it has been a long time since I have flown them
.