You might want to check this one more closely.

When your recast timer for light shot expires, are you able to use the ability straight away, or do you still have to wait until 4.5 seconds after you last used the ability for it to actually work?

I say this because there is a known bug that causes recast timers to incorrectly display, with the deviance from the advertised time slowly increasing every time you cross server boundaries within the game (ie: from Emerald Moss to Treespeak or from northern Ul'dah to Central Thanalan). The bug doesn't cause the recasts themselves to change - just their display. The bug is resolved by restarting the FFXIV client.

Of course if that is not what you are experiencing, we may indeed have a loc error on our hands (I don't play archer so I wouldn't be able to test this myself).