It never ceases to amuse me how confidently "it's difficult to define" and "clearly it's this way" can appear in the same thought/sentence about the mind.
Yes. Something can be difficult to define exactly, yet also have clearly recognizable features. You haven't thought about it very hard if this "amuses you".
No, you dohave a valid list of features you want to group together, but attaching them to a word you have not clearly defined -- especially in this incredibly fraught case -- is just confusing you. If you haven't decided on a definition, you can't agree on a definition with anyone you are conversing with, and you will just talk past everyone. That is how this topic usually goes.
There's not some objectively true definition or there that you are homing in on with your intuited features.