The lack of definitive information seems surprising for what must have been a prominent monument in the local landscape. The location today is open access land but presumably was not always so accessible. Cothelstone House (not to be confused with Cothelstone Manor, which is still standing) was demolished in 1962.
The sad remains of Cothelstone Tower - looking west towards Will's Neck and Minehead
Looking south east towards the Blackdown Hills
Somerset Follies by Jonathan Holt. Published by Akeman Press in 2007