Hello AncesStory,
Searched nls. maps but not been able to pinpoint Water Mill, however, I did find one or two references which makes me think Water Mill is in the Carsebridge, Alloa area of Clackmannanshire.
Found an 1881 Census for a Coalminer named David Ramage living at 15 Watermill Row, Carsebridge, Alloa, Clackmannanshire.
A Clackmannanshire Field Studies Society Newsletter that mentions the 6th Earl of Mar's Lade which ran on an East to West axis, carrying water from Gartmorn dam to "de-water his coal pits at Holeton and Water Mill etc." (Water drove an engine which pumped water from the pits)
Gartmorn Dam, built in the 1600s by Sir John Erskine, 6th Earl of Mar (1675 - 1732) was heightened in 1785 and by the 1860s water from the lade was powering 3 colliery pits and 11 water wheels at various mills. I've often walked my dog along the lade from Forest Mill to Gartmorn. A beautiful walk and an impressive piece of engineering.
www.engineering-timelines.com/scripts/engineeringitem.asp?id=1342 Last but certainly not least is this find. National Records of Scotland at Sighthill, Edinburgh have an 1853 plan of of Alloa Colliery, Clackmannanshire. Ref: RHP151/2.
This plan includes Reekie Row, Nos 1 & 2 Holeton Engine, Keilarsbrae, Water Mill, Crandraw, Peacock & Old Pits. Distillery, colliers' houses, school, Keilar's Brae works, aqueduct from Gartmorn dam Upper & Lower Carsebridge, Whins & Hall House.
http://catalogue.nrscotland.gov.uk/nrsonlinecatalogue/details.aspx?reference=RHP151/2& Unfortunately, you can't view the plan online but it can be viewed at NRS, Sighthill.
Good luck with your search,
Regards, Dod.
Added. The Lade from Forest Mill to Gartmorn Dam diverts water into the dam on the east shore of Gartmorn. The mill lade or race which drove the pits & mills is on the west shore of Gartmorn.