To clarify,
light weapons include dagger, short sword, light pick, light hammer, light mace, sickle, hand axe, and kukri. Rapier does not count as a light weapon, but is an exception which is affected by weapon finesse.
The second tempest core allows you to treat scimitars as a light weapon and to use your dex modifier for to hit with light weapons, which does not include rapier. The third tempest core allows you to use your dex modifier for damage with light weapons, which now includes scimitars but still not rapiers.
Improved weapon finesse from deepwood stalker allows you to use your dex modifier for damage with any weapon that you can use your dex modifier for to hit. So in order to use dex for damage with a rapier as a ranger, you need to take the weapon finesse feat (which allows you to use dex for to hit with a rapier) and improved weapon finesse in deepwood stalker.
The feat requirement for improved weapon finesse was removed so that the enhancement could enable dex to damage with bows (the elf tree is the only other way) and thrown weapons without requiring ranged builds to take a melee feat. But if you don't take the feat, then you won't get dex to hit with rapiers. So if you want to use rapiers and get dex to damage, you still need to take weapon finesse and improved weapon finesse. In fact, before improved weapon finesse included bows and thrown weapons (i.e. before the revamp), the
only weapon it really affected was rapiers, because why would anyone who intended to melee not already be taking the second and third cores of tempest which allowed dex to damage with every other finesse-able weapon and scimitars (the slashing equivalent of rapiers).
So rapiers are a poor choice because they require a feat and 1 AP to get what scimitars get for free. The only problem with that is there are much better named rapiers (e.g. Balizarde) than scimitars, but that doesn't really matter near endgame when crafted weapons are the best option.