Hi Fiona g
Cannot see anything on your William or Jean. They may perhaps be buried in Gladsmuir, which is very near Elphinstone, but unfortunatly I don't know of any MI's published.
Other Burnsides are
Stenton
by Archd Burnside in memory of father Richard Burnside 8.5.1865 77yr (wife Jean Bell 16.11.1828 38, son John 26.8.1838 8yr,and 3 family died in infancy, 2nd wife Alison Elliot 12.3.1845, 51yr, daughter Janet 11.5.1886, 62yr, daughter Alison 11.4.1892, 80yr) Archd Burnside 18.7.1900, 64.
Innerwick
47
father John Burnside, died thornton 10.4.1867, 76yr, mother Isabella Outerson, died Thornton 16.8.1875 83yr, by son Alexander(newphew Archd Welsh died Crowhill 17.8.1862, 16month) sister Marg Burnside died Tansy-bush 14.3.1898, 65yr
48
by george Anderson died Redheugh 17.3.1901, 80yr, in memory of Elizabeth Burnside died Thorntonloch 19.4.1889, 64yr
153
by John Watt, Spott in memory of neice Ann Watt Sanson 19.2.1858 7yr, sister marg Watt 8.9.1863, mother Cath Gow 22.6.1865, nephew John Watt Burnside, died Pinkerton 15.5.1870, Father John Watt 22.3.1881
220
David Burnside 14.4.1919, 68yr, wife Mary Samson 22.9.1904 77yr, son Thos 11.3.1873 9yr.
These are all the Burnsides I can find in the books that I have, hope this helps some
Fiona