"Believe in me" in the Gospel of John

In the Gospel of John, Jesus says "Believe in me" often. In the other gospels he doesn't do this. What's going on?

Firstly, I wish to make the point once again that pistis "believe" ought to be rendered "faithful" or similar, and has notions of allegiance and faithfulness rather than intellectual belief. Further evidence on this subject has recently come to my attention: The second century AD writer Arrian of Nicomedia, twice writes in his biography of Alexander the Great that certain people remained "pistis" to Darius (Darius was their king), and the Loeb English translation renders this "loyal to Darius", which is clearly what is meant in the context. (Anabasis III.21.4 & III.23.7)

How are we to make sense of "be loyal to me" in the mouth of Jesus? Why is it in John and not the other gospels? The answer I think, is that it is in the other gospels, it's simply worded slightly differently: as "follow me".

One of the things I think Jesus was intentionally doing during his ministry was forming a movement/group/sect/cult around himself. He and his disciples recruited followers into this movement and we see in the gospels in the form of Jesus asking people to "follow me".

So why does John have "be loyal to me" rather than "follow me"? Part of the answer is probably that Jesus spoke in Aramaic and the gospels are written in Greek, and the gospel authors used slightly different Greek words in their translation.

However, I would go further and suggest that here the Gospel of John is being anachronistic. ("Anachronistic" means not keeping proper account of time differences, eg reading an ancient text with modern assumptions, importing your own meanings into an ancient writing etc) Jesus in his own day would have want people to physically follow him around and/or actually join a movement physically led by him. For later Christians this would obviously be impossible. Their equivalent of "following" Jesus was to be loyal to his name and cause. They could not physically follow him, but they could be loyal, committed and faithful to him. And so, the writer of John, understanding this as what Jesus would have said to the Christians of the writer's time, records Jesus as saying "be loyal to me" rather than "follow me" to those around him. This is a fairly basic anachronism, which the Gospel of John is recognised to be particularly prone to.