Unfortunately we know very little about young William as the only evidence of his existence are his burial details. From this we know that he was buried at St John the Evangelist in Lambeth on the 22nd May 1827. His age was given as 5 months so this would put his birth in the December of 1826.
It seems most likely that he would have been the son of Daniel Chrystal and Martha as on the other side of the family (Frederick Gottlieb's) Charles was born in the February of that year and baptized in Bloomsbury on the 8th of May. If Frederick had been his twin surely he would have been baptized at the same time especially if he was ill. It would also make him 3 months old at the time of his burial.
Old drawing of St John the Evangelist.