It is my opinion that the "Blind Half Hundred" name was simply adopted from the Kent Regt of the British Army and did not relate to the medical condition of the 50th Ill Regt. It was probably named by a senior officer of the 50th Ill or higher Hq with either a geneological or historical connection with the Kent Regt.
William H. Horton at the age of 16 joined 'B' Co. of the 50th in Jan 1864 as a Private and was mustered out with the unit in July 1865. In 1871, he went to Montana with four or five persons who served with him (identity unknown but I am curious). He settled in Columbus, Montana and is credited with writing the first newspaper article recording the defeat of Custer on the Little Bighorn. His home in Columbus is on the Register of Historical Places and an effort is underway for its restoration after some years of neglect.