According to 'The Old Stones of the Cotswolds and the Forest of Dean' by Danny Sullivan (1999), the Twizzle Stone is at this grid reference. It's ages since I've seen the book so can't describe it further - the stone is not on Magic and (seemingly mistakenly) I always assumed this and the Tingle Stone were one and the same - similar names I guess.
Mr Grinsell is describing stone that turn round, when he says "We may perhaps also compare the Twizzle Stone in the Cotswolds, which, I would suggest, may have twizzled round when it heard the cock crow." Ah the world of speculative folklore, I love it.
Tom Graves has a more concrete story. He is talking about different bands of alternately 'charged' areas on certain standing stones and other sites.
The [bands from the fourth up] connect up with other energies, or networks of energies, above ground; and in the case of the fifth and seventh bands, this connection, as far as many dowsers are concerned, produces some interesting side-effects.
The effect of the fifth band on the dowser may have given a standing stone in Gloucestershire its name: the Twizzle Stone. When a dowser leans against the level of the fifth band on a stone or buttress, the band somehow affects the dowser's balance, producing an effect which feels like a slow and gentle push to one side or the other.
According to the skill of the dowser (and, it must be admitted, more subjective factors like a sense of showmanship), this sense of 'being pushed' can be increased until it looks as if the dowser has been thrown to one side by the stone.
Well if you can find it maybe you can check for me.