I consulted on Eyslk with a friend who is an expert on Welsh names and here are excerpts from her reply:
Eyslk must be an error for Esyllt. It might be a form of Cornish Yselkla. pronounced izella (can't remember whether this is a form of Esyllt, but I think it's not, it's a modern Cornish vocabulary word - Check 'Names for the Cornish' if you have a copy). But it's definitely not a Modern Welsh form - it might have come from someone writing down the pronounciation of Esyllt for a non-Welsh speaker.