Morning Anne. Well as promised I searched al over my data for your family.
Whereas I cannot find a connection to mine .I would not rule out a possible distant relation-not many Seggies around!There were a couple of Seggie clans i found around 1785 from a connection James Seggie and Isobel Kinlock-Midlothian Seggies.I have bumped head with this family before and discounted it was not MY connection.In this family were a couple of naming patterns from your inquiry-Peter [1779],James [1785]also Patrick[1787],Janet 1790] and another'Janet-[1792]My reason for discount was A Names Peter and Patrick never popped up again and Mine were C of Scotland, these sounded R.C.!Other reason is occupations. Mine were mostly farmers,clerks shop /trade workers.I raise this because out of curiosity I did a search on your William and found generation after generation miner stock.
I am not sure how much data you have on you side and I will willing share what I found, if you are intersted. Basically I found the fmily living in 1891 census in Kilmaur,DOB given abt 1855!]:also 1901 Census .Willaim was married 2 times once to Elizabeth McCrae and later Margaret McIllravy.9 children total.I found a William born Jan ] 26 1855 Slamman Stirling [a minning community] to a William Seggie and margaret married 1842.I also found this couple in 1871 census Kilmaurs with family Robert [1851 Lanark]Peter [1853 Lanark]William*1855 Linlithgow],Margaret 1857 Linlithgow],Mary 1860 Lanark Glasgow] and Isobel 1862 Lanark Glasgow] Again there is that naming pattern. anyway I am not closing door to a distant relation but at present I have nothing.let me know if you need any further info.
Sheena