Hello Hilary,
Yes, my family is the Morrow line. I found the wills of John P senior and junior on Ancestry. They are also available from the National Archives. A copy of John junior's will is also available on Scotland's People, since he died in Scotland. The Scottish version is actually easier to read, and includes an inventory. I ordered the Family Search films for Norham St Cuthbert, Norham Presbyterian and Ladykirk (just across the river Tweed in Scotland, where the established church is Presbyterian), but couldn't find a baptism for William, nor a marriage for his parents John & Margaret. Interestingly, the Presbyterian record for Norham shows John Palin (sic) under 'admission' on 28th June 1772. I assume this means that he joined the church on that date. This was just 3 days before his son John was baptised. Is this significant? Had John senior just joined the Presbyterian church, or had he just recently moved to Norham from elsewhere? If he had moved, then it would explain why I haven't found William's baptism, as I believe William was born a few years earlier, probably about 1768. Someone called Mike Simpson has kindly posted online details of Pallen burials in Norham: 'In memory of John Paulin of Norham who died ... November also Margaret his wife who died March ... 81 years. Also Diana Williams wife of John Paulin their son died in London January 5th 1830. Also the said John Paulin their son died in Dunse 19th April 1849 aged 77 years.' Obviously the headstones are worn and not completely legible. But the St Cuthbert register shows John senior was buried 3rd December 1831 aged 84. I haven't found Margaret's burial. I believe she probably died some time between 1832 and 1838, as these years are missing from the register. I'm going to WDYTYA live next week. Maybe I'll pick up some ideas as to where I can look for more clues.