Jay,
It is implied by the fact that the person wants to be baptized and has expressed that intent.
OK. That makes sense in that a person who didn’t want to be baptized wouldn’t present themselves for baptism. (Which is what deceased non-Mormons did (or didn’t) do while they were alive. They did not believe in Mormonism so they did not present themselves for baptism.)
Again, the fact of their becoming a “member” is because their name is recorded, but the covenant making is between them and Jesus Christ, and the Holy Ghost is given to them individually. I wouldn’t use the word “solidifies”, but rather “formalizes and brings into covenant”. It is implied that the person “believes in the Mormon faith” to the extent that they believe they need to be baptized and that the Mormon priesthood has the authority from God to do that. But it does not mean “per se” that they believe every single thing that they are ever going to hear or read about beliefs of other LDS members. Baptism is a fairly simple covenant, and it is with Jesus Christ, not with other people.
Then why are non-Mormons who are “baptized by proxy” not members? - their names are recorded the same as live Mormons who have been baptized, the entry just says baptism by proxy as opposed to just baptism.
And I also understand the covenant is between the deceased and God. If the baptism of a living person “formalizes and brings into covenant” that person, why does it not do the same for the deceased person?
That was already implied by the fact of their wanting to be baptized.
If you have followed the last couple of days back and forth exchanges, it is because if Mormons truly believe they have authority from God to perform necessary baptisms to provide entrance to the gate of salvation if the person chooses to enter that gate, then to withhold that entrance because a person didn’t understand the implications during their mortal life would be to make a decision for the person that the person should be able to decide for themselves, when they have understood what the decision really is.
Do Mormons believe that God will not accept a person if they have not gone through a baptism either on earth or by proxy on earth? Somehow I find that position to limit the power and mercy of God. Or maybe the Mormon view of God is so vastly different from my view that I will never be able to make comparisons and reconcile the two.
If you will separate the decision about “being a Mormon” from the decision about “covenanting with Jesus Christ”, then I think perhaps you will be closer to understanding the perspective.
So then the baptism of a person is NOT what makes a person a Mormon? A person can be a Mormon without undergoing a baptism?

Sorry, but you’ve totally lost me here. As a Catholic, I have a relationship/covenant with Jesus Christ. Why, when I am dead would I then need another one through a “baptism by proxy”?
If it still appears that way to you, then I hope you’ll go back and re-read several of my comments and those of Dianaiad. Your assumption is simply not true.
I guess I just don’t see/understand the position then of the person doing the baptism. What are they declaring or doing by undergoing a baptism by proxy? I will go back and reread your posts. I have a tendency to skip over some of the more “snarky” responses made by some people and in doing so I may have missed something. Offhand, I don’t recall reading anything that made sense, thus my current set of questions.
There is not a difference. You would need to understand the component of faith expressed during covenant-making. To introduce such an “iffy” kind of clause, expresses doubt and decreases the active power of faith. When such a spirit person accepts the ordinance, they will be doing it with full and complete faith in Jesus Christ, not an “iffy” kind of faith.
The “iffy” part would only be on the part of the acceptance of the deceased person, i.e. “We are performing this baptism for so-and-so **in the event **they will accept this offer of a covenant with Jesus Christ according to Mormon doctrine etc.”. The “iffy” part is supposed to be because one does not know if they accept or not. I was under the impression that no one knows and that Mormons don’t make any judgment as such - or do Mormons operate under the notion that all deceased people
will accept such a covenant if it is offered?