My neurologist is a cyclist and had also had a bad concussion from a crash. He forbid me from riding on two wheels for a month. The 2nd concussion on top of an unhealed one is too risky for quality of life in the long run.
So, I had a month off. Hit the trainer about once every 4 or 5 days during that time. Just 30 minutes of tempo. That felt like a pretty solid recovery. There were times in there where my hunger went through the roof, and I just ate based on how I felt. I was eating a bit more than I did in training. The fact that I gained no weight tells me that it takes a lot of energy to heal a brain injury.
When I came back on the bike, first week I was winded. 2nd week I was able to complete some intervals. 3rd week and I was clearly coming back. I think that month off really helped.
I'm no doctor, but I'm surprised that so many are given the go-ahead to ride immediately after a concussion. That risk of a 2nd one just isn't worth it, and the forced recovery can't hurt (assuming you don't go all-out on the trainer).
Sometimes I find myself in the pantry wondering why I walked in there. I can't remember for sure, but I think I did that before the concussion as well though