Simple solution. What James taught Jesus had already taught. The prayer of faith that James talked about in Jm 1 and 5, is found in Mk 11:24. Mark 6:13 says as well in the gospels that the disciples would anoint people with oil to heal the sick.
I'm sorry but that is definitely reading into the text.
How is;
Is anyone among you sick? Let them call the elders of the church to pray over them and anoint them with oil in the name of the Lord. 15 And the prayer offered in faith will make the sick person well; the Lord will raise them up.
the same as;
Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours.
In the first one it is the elders of the church who pray.
In Mark 6 there is no church and it is the individuals themselves who are praying
It wasn't that long ago that you said:
But you're under the impression that a minister can just lay hands on a believer and God will heal them regardless as to what the other person is believing. Generally speaking that's not how it works.
James 5 doesn't say anything about the other person having to believe, or have faith.
If you read James 5:15 it is the prayer,
offered by the elders in faith, which raises a sick person up. If you read Mark 11:24 it is the person who is praying who needs to have the faith.
I don't see how both can be true.
If someone is praying, as per Mark 11:24, and they receive what they have prayed for (healing is not mentioned here), they could say that they received because THEY believed. The elders of the church have not been involved. James 5 wasn't needed.
If a sick person calls the elders (or equivalent) of their church to pray for them, as per James 5, and the prayer of the elders heals the sick person, it doesn't matter what that person believed, or even was thinking about. The sick person did not have to believe as Mark says, because it was the prayer of the elders which brought healing. I read a testimony of a mother who, on several occasions, took her sick baby to a healer for prayer. The baby didn't believe anything, and most of the time he was asleep, but God healed.
There are many accounts in the Gospels of people being healed without their having to declare faith and irrespective of what they believed, or were thinking at the time.