Always difficult if Annan was a common surname in the village of Dunshalt. Curiously I was looking at valuation rolls on Scotland's people website recently, in 1855 there was an Alexander Annan shown as proprietor of houses and gardens etc, Dunshalt
Might (not) be related to a family of Annan in Dundee (1840s show vintner/grocer) but later mason/builder assuming the same Alexander Annan. One of the children's names was Ebenezer and possible although definitely not certain there were connections with Auchtermuchty.
Only recently learned from the land tax rolls (1820) there were two ridges of land at Dunshelt, purchased by Ebenezer Marshall and possessed by Alexander Low.
(Coincidence or otherwise, in 1829 a marriage of Ebenezer Annan and Margaret Low)
https://scotlandsplaces.gov.uk/digital-volumes/historical-tax-rolls/land-tax-rolls-1645-1831/land-tax-rolls-fife-volume-05/33Annan cottage
https://canmore.org.uk/collection/2400767