I am also researching Pake's from West Lothian and would love to share information etc.
I have also found various spellings of the name and feel sure that it is down to the fact that the name was written at various times by various people who spelt it however they thought it sounded i.e. differnt census enumerators, registrars etc. As there was a good chance early on that the person saying thename was illiterate then it would be up to the person who wrote the name to spell it, so variants would have crept in. Thats just one thought on it though.