how do you know ? - I'm sorry if I've missed it but maybe a brief resume of known facts might help especially if it gives any leads to a parish.

I have a database put together from IGI and my own transcriptions but no William Gale in that period - there are 4 William Gells - one of whom I can discount as he settled in Peel by the 1851 census but the other 3 are not 100% identified.

It might be possible he claims manx birth though bought to the Island as a baby -- it may be possible he was illegitimate, the IGI would list him under mothers name but by Manx custom he would be known under father's name.
There are some 150 Williams at least christened in that 2 year period.

However as you are finding brick walls are fairly common in genealogy .