Isabella death could be a possibility but no trees attached. 1877 would have been not long after the last child Sarah Thomson was born in 1874. Maybe Margaret born 1858 - the oldest child helped raise the family. I can't find her but could be because she never married?
Death of Robert Thomson - his name is wrong as William didn't have Robert in it.
I wouldn't discount this set of deaths. Your William Thomson is a stone cutter on the 1870 Census. This set of entries on the city directory shows that there was Wm Thomson who worked with stone alive during the year May 2, 1878 and May 1, 1879. But was not alive during the year May 2, 1879 and May 1, 1880. The man Neale1961 found died July 20, 1878, and is buried with an Isabella, both born in Scotland and both ages close to what the 1870 census says.
** NYC City Directory
*** 1877
William Thompson, stone, h 343 E 24th
*** 1878
image 5 says "for the year ending May 1, 1878"
William Thomson, stone, h 504 W 50th
*** 1879
image 5 says "for the year ending May 1, 1879"
William Thomson, stone, h 504 W 50th
*** 1880
cover says "1879-1880"
image 5 says "for the year ending May 1, 1880"
William Thomson, stone, is not listed
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Have you found the family in 1861, presumably in Scotland? Any births for the 3 older children ? Wm & Isabella's marriage?
I'm fishing for a record that calls him Robert or William Robert. The son born in Scotland was William Robert and he named at least 2 sons William Robert, so maybe the man who married Isabella was also a Wm Robert.