Note that gameObject.GetComponent is not neccessary, it does the same thing as just GetComponent.
If by ThisComponent you mean the current MonoBehaviour, you don’t need to store it, ever, as it’s available through the keyword ‘this’.
If you want to store reference to a script, but don’t know the exact type of the script, you’re looking for the class MonoBehaviour, as that’s what all of the scripts that you can attach to GameObjects inherit from. So that’d be:
private MonoBehaviour storeHere;
Though that’s unlikely, as you won’t have access to any of the methods or variables defined in the script.