All sniper rifles have a 2 second combo duration, with the exception of the Lanka, which has a 6 second combo duration. Harkonar Scope at max rank extends this to 14 seconds, and to 18 seconds for Lanka.
The extended combo duration only applies to a stack if the player is already scoped when the previous stack expires. As such, the most efficient combo conservation can either be achieved by always being scoped in, or only every 14 (18) seconds, when the counter decrements.
This mod, along with the other Executioner mods, are the second set mods to feature non-generic enemies on the mod card, the first being Vengeful Revenant.