The National Probate Calendars start in 1858. It is an annual alphabetical index by year of probate. An individual is recorded when a will is probated or Letters of Admin are granted.
I recorded my Tinkler info on my various visits to the Lincolnshire Archives or the Lincoln probate office. Most of the info was on fiche which provides quick access. Since they have consolidated wills at York, I don't believe that the Lincoln Probate Office provides public access to their indexes.
I know that the LDS have films of the earlier years; but, you need to know the year of probate. For most individuals that I recorded, it was the same year as the year of death. When death occurred very late in the year, the will was usually probated early the following year. The older indexes provide an considerable amount of info. The most recent years are very sparse.
The marriage of John William TINKLER & Isabella HUME was recorded at Auckland during the 2nd Qrt of 1901-page 402.
Do you have dates of birth for the other children? Here is what I found in my Civil Reg Birth Indexes:
Albert 1st Qrt 1904 John William 4th Qrt 1908 Jennie H 4th Qrt 1913 Mary 3rd Qrt 1920
All the above births were registered at Auckland.
I can't spot an entry for Ethel.
Given the large gap between Jennie & Mary, was John William in WWI?