I had a random flash of thought. Having dealt with pigeons for a great majority of my life, I encountered many neurological problems that afflicted baby birds, often translating from viruses or bacterial infections. There are cases such as this that can not only be picked up from the environment but through the pores of the egg and from the parents in the case of a virus, which seems most likely, it is likely spread to young through their eggs, or from their parents or other birds that are around them. What I remember most clearly is PMV, or Pigeon Paramyxovirus, which causes somewhat alarming neurological side effects that include twisting of the neck and "stargazing". From the looks of things, Paramyxovirus is not limited to pigeons, and there seem to be many different strains of the virus, some more or less severe. Some strains may only cause neurological symptoms while others cause digestive issues, as well, including diarrhea of a greenish color.
What I remember most clearly is that the birds may act normal unless they are eating or drinking, when most of their symptoms show themselves.
Oh, and you mentioned that his head never seems to sit still? That is another symptom head tremors. Here, watch this video and tell me what you think:
Also, as there are many different strains of the Paramyxovirus, it is likely your baby has a lesser one that may not be fatal, but manageable. I know of many people who nurse birds such as these throughout their lifetime. Sometimes, birds seem to make an almost full recovery. However, sometimes the disease causes long term neurological side effects. If this baby is not dying while others birds did, it seems likely it is the strain which is different, more deadly than the one you are seeing.
