The good thief did not just have faith; he had Actions. He roused himself, rebuked the mocking bad thief, and publicly stated his faith in Christ and asked for mercy.
He had faith with works. This is what Catholics believe saves us. We must live faith out daily through our actions or we are like the fig tree that bears no fruit. Every time we resist temptation and turn away from sin we are “born again” in Christ. In baptism, we become children of God. In Confirmation, we become adult believers who affirm, as adults, that we belong to Christ alone. Confirmation is the completion of baptism.
One can also be baptized through desire, as the thief was, if there is no other way for a baptism with water. Nothing is impossible with God. If we knock at the door, He will answer.
Catholics do not believe one achieves salvation at one moment in time, but throughout a lifetime of choices. What happens to people who are born again, but then backslide? What if that backslider lives a life of complete evil right up to death? Is he fit for Heaven and unity with the purity of God? No. His choices are what he will be held accountable for at his moment of judgment. His life showed he was not saved. We send ourselves to Hell.
As for the person who converts at the moment before death, I believe he is saved, but not if he plans it that way. Then it is not a deathbed conversion but an attempt to hoodwink the Almighty.