No map references, unfortunately. This is a 2006 publication, not the earlier book published in 1977 which was just on field names, and which I do not have.
Beckensall provides detailed plans of fields for some other places, but not for Elsdon.
The fields are not in alphabetical order, but in case they are are in geographical order, I will also list a few names either side of Spartyshaw.
The section starts off as follows:
"Elsdon, Monkridge, Woodside, Troughend, Otterburn & Rochester
"Two abbreviations used here are: A for "Ancient Land" and C for "Common Land". All fields are both Ancient and Common, unless A or C appears separately. All are from the nineteenth century. Meaning are given in the general index.
Elsdon Ward"Elsdon has a very large village green, reminding us that this was a focal point of drove roads along which cattle were driven from Scotland....
"....Whiskers Shields, Harthouse, Hudspeth (path), East Nook & Colsters, John Croft and Spartyshaw, Elsdon Gate Cheek, Bainshaw Bogs (C), Redshaw, West Tod Holes, Bird in Bush Inn, Glebe Lands, Whitlees and Lea Houses...
"This impressive list of names contains many that hark back to the rig and furrow systems of arable farming..."
I am inclined to think some association is intended between John Croft and Spartyshaws, as "and" is not used all the time in the list, but that is my interpretation only.
I could not see Spartyshaw in "Northumberland Place Names, Goodwife Hot & others" by Godfrey Watson.
Perhaps the OP would like to browse amongst the many old maps available on line. Google will bring some options up, including the main site for Ordnance maps but here is another one -
http://www.visionofbritain.org.uk/place/9101Someone gave the reference for the National Park Historical Village Atlas earlier, for Rothbury. Elsdon is also included in this project, and there should be some useful info and hopefully map references. Unfortunately I cannot access this site at the moment. Maybe my ISP is having problems again.
As the OP's ancestor was eligible to vote, and some in his family had sufficient worldly goods to leave wills, I am assuming that at some point along the way they managed to put up at least a bothy amongst the scrub