This is what I've been saying from the beginning...
every example will be incorrect in some way or other.
I've been reading that link you sent and, my goodness, I do sound like a modalist, don't I?
I had asked you your understanding of the difference between modalism and trinitarianism because what you posted did not include my understanding of the difference, which is this:
Modulism states that the 3 "forms" of God did not always exist, but were created out of necessity at some point in time.
Trinitarianism states that the 3 "forms" of God always existed and were never apart from God (Father).
This makes understanding modalism easy for me.
YOU have made it more difficult !
If I may be so bold as to say that the fact that you understand modalism so well is the reason you stick to every word that is said. You're able to spot it a mile off.
Most of us do not understand it so well and so it's a little easier to speak about something that is almost non-speakable.
How is this in your opinion: I think it explains it really well.
The Trinity is the term employed to signify the central doctrine of the Christian religion — the truth that in the unity of the Godhead there are Three Persons, the Father, the Son, and the Holy Spirit, these Three Persons being truly distinct one from another.
Thus, in the words of the Athanasian Creed: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God." In this Trinity of Persons the Son is begotten of the Father by an eternal generation, and the Holy Spirit proceeds by an eternal procession from the Father and the Son. Yet, notwithstanding this difference as to origin, the Persons are co-eternal and co-equal: all alike are uncreated and omnipotent. This, the Church teaches, is the revelation regarding God's nature which Jesus Christ, the Son of God, came upon earth to deliver to the world: and which she proposes to man as the foundation of her whole dogmatic system.
source: https://www.newadvent.org/cathen/15047a.htm