So, I agree with Anarch about the two possible implementations: consumable or UI.
The consumable item option would be fine since TL1 is single player; you don't have to worry about multiplayer compatibility with this mod. The only hard part is that, if setting the base file to consumable doesn't change all the others, you'd have to manually change all the different ember items to 'consumable'. Then you'd want to add an effect to each ember to make it add to a custom stat (like Anarch said), and you'd probably want to modify the value by quality of ember (+1 for a speck, +5 for a flawless perhaps?) That might take a little time, but not too much.
The other option, the inventory slot, is done through the UI and the Slots/Containers editor. This wouldn't require a skill. Instead, you'd use a logic group to remove the ember and add +1 (or whatever value you wish) to a custom stat that records how much ember you've eaten. This solution might take a little more time.
I also agree about using a custom stat. This way, you can also create a graph to control how much of a stat boost the character should get from having eaten a certain amount of ember. Maybe you want it take 1 Core ember to give +2 Str, but 100 Core ember to give +5 Str (just for example). You can do that by having an Effect set to the character that gives a bonus to Str based on the (just a suggestion) Core_Ember_Eaten stat.
Now, I'm assuming that you asked...
1. Is there a way to make a skill able to target certain kinds of non-equipment items, but not others? If so, how?
2. Is there a way to make a single skill behave differently depending on the name of its target? If so, how?
3. Is there a way to make a skill override an entity's internal properties (for example, the "invincible" flag)? If so, how?
4. Is there a way to change a skill in TL1 so it uses stats instead of levels as a prerequisite? If so, how?
5. Is there a way to make a skill check the properties of the current area, such as whether town-portals are allowed? If so, how?
...because that's the setup you imagined for creating an 'ember consumption' mechanic that adds to your stats. But like Anarch and I have outlined above, I don't think #1-4 are actually necessary.
Just add one effect to your custom class per ember effect (so, one effect that adds Str per Core Ember eaten, another for Fire Res based on Fire Ember eaten, etc). You'll also want one custom stat per effect, so Fire_Ember_Eaten, Core_Ember_Eaten, etc.
As for #5, I'm not sure. Why do you want to do this? There may be an alternate method.