I have a John Baily in German Confirmations 1793 - that year they were listed under Peeltown and Parish - he was in Peeltown - you needed to be about 14 to be confirmed
but I can't find a bapt) - in IGI under German PR batch num (c038151) are Catharine 1784, Edward 10 JAN 1786 (d. 1789)and 22 NOV 1789
Catharine is in the 1799 confirmation list (under Peeltown).
William is only found in Igi under a 'sealing for the dead' and dated bapt 09 DEC 1787 - to be honest I generally give zero credence to these however there is a putative death date for a William 1789 which corresponds to a will so I suspect the submitter has done some homework; the date is possible with a 2 year gap between conceptions - there is an infant burial of a William 11 Jul 1790 which would correspond - I transcribed the German bapts upto c.1756 (I will work forward over this year) and found the igi had removed some PR batch entries and replaced them with 'patron submitted' (a re-reading I think of the 1911 transcription) as some obvious erroneous readings as seen in the original PR had not been corrected but these patron submitted corrections usually corresponded to genuine entries in PR - a 1787 bapt should mean he appears in a confirmation list c.1800 - I have a copy of the 1803 list but havn't transcribed it yet (& I think I left it in Peel) - however there is a 1814 census of peel which assuming I transcribed corrected has 2 Bailie families - a Jno with no children (just 2 adults) + Edward with children - the numbers correspond to the known people - however it is possible that the ? William arose from either a re-reading of the PR or an entry in a will but if William was present in Peel in 1814 I would have expected to see him thus I assume that William was dead by then (didn't see a 2nd william except an unrelated child in Braddan).
As I can't find a baptism for the John who appears in two indep sources then one explanation is that he arrived as a small child in Peel which places William snr's arrival between 1780 and 1784 - there might well be no connection with Alexander