Hey rokurota, loving all the Boshin war work you are doing on this page mate!
My Japanese is not native level, but looking at the Japanese wiki page for the Gakuheitai I gleaned a few things.
The uniform was a British design made from felt and was reversible, from what I understood it meant that one side was red and the other black? Was there a British uniform like that in service around this time?
There were approximately 800 soldiers in 6 platoons (may not be correct terminology) and most soldiers were the second or third sons in their family. They also apparently had a military band!
I am trying to read through the units military history (if you are interested) but need to finish a job application before getting to it (a fair few kanji i dont know so I will need to go through it closely). It looks like the units leader, Juntaro Hoshi, was a pretty interesting character too! It looks like he was frustrated by Sendai joining the Northern Coalition so the Gakuheitai captured Souma Castle on their own initiative. Apparently his own higher ups had a plan to assassinate him which was eventually vetoed! After surrendering apparently the Gakuheitai were offered sake by the enemy but, fearing it was poison, didnt drink it until Juntaro laughed and downed a glass!