I saw the will of John Dixon of Shotley. Thanks for pointing it out and also taking the time to search around on my behalf! That 1750 will for John Dixon names his wife Isabel and sons George, Edward, Joseph "of Stanhope," and William. The sons of John Dixon that are listed as baptisms in the church register from Shotley are Joseph (1715), and William (1720). Then in 1726 there is a death of John Dixon son of John, which would explain why there is not a son John Dixon in that 1750 will. William is my 5th great grandfather ("son of Jno. (John) Dixon" in his baptism record in 1720). Edward Dixon is not in the baptism records, nor is George, however, in 1740 begin a series of baptisms of John, George and Joseph, sons of Edward Dixon. I assume that the will names the sons in order of age. This would mean that the older 2 sons were probably baptized elsewhere, and they moved to Shotleyfield around 1715 or before, or the earlier baptisms were simply not recorded (the register for earlier years seems to be incomplete, as it contains far fewer records than in later years). Then, there are baptisms for children of an Edward Dixon starting in 1740. That timing seems to jive with him being an older son, as that is only 20 years after the birth of William...I assume that Edward was older than 20 when married, which as you mention seems to be the custom at that time, probably to help the parents raise the younger children and help the older parents with farm work, etc. Also, the children of William Dixon include Isabel, John, Joseph and George, all names repeated in John's 1750 will. As we know, they often named their children after parents, then uncles of the children (siblings of the parents). There is a death of Isabel "wife of John Dixon of Shotleyfield" in 1751, which is after John's 1750 will was made, but there is no record of an update to that will after her death, although it really would not be necessary as the will simply calls for a regular stipend to be paid to Isabel until her death. Also, John's marriage to Isabel is not in the Shotley registers, I believe we discussed this already, as you noticed a marriage of a John Dixon to Isabel in the register of St. Andrews Bywell. This also jives with no baptism either in Shotley records for the oldest sons Edward and George. I need to search for a baptism of a George and Edward Dixon shortly after the marriage of John and Isabel there in Bywell.
John Dixon's will you mention was written in 1750 and probate in 1764, I believe. The burial of "John Dixon of Shotleyfield" was in 1763, as recorded in the Shotley register. Probate in 1764 would be reasonable.
The admin bond you see for William Dixon of Shotley in 1769 is indeed for my ancestor, who died in 1769. He died without a will, and the record you cite mentions that his widow Elizabeth must submit an inventory of the assets of the late William Dixon within 6 months. Indeed, there is a much earlier marriage of William Dixon to Elizabeth in the Shotley register, so this all jives.
Bottom line, I have a pretty good degree of confidence that the 1750 will is that of John Dixon, my ancestor, especially since his son William is also of Shotleyfield, which is a small hamlet about a half mile south of the St. Andrews Shotley chapel on Kiln Pit Hill. I feel that the marriage of John to Isabel Dixon and the baptisms of older brothers George and Edward Dixon either occurred elsewhere (perhaps Bywell), or were simply not recorded in the Shotley register since I noticed that the records in the Shotley register were rather sparse in the years prior to 1715 or so (perhaps they were not good about recording everything at that early date), and there is nothing in the register before the late 1600's. Any further thoughts would be welcome, and thanks again!