According to ‘Household Tales with other traditional remains’ by Sidney Oldhall Addy (1895), the Eagle Stone turns around when the cock crows (p56).
The book may be seen online here.
Stubob’s ‘Aigle Stone’ idea maybe comes from here
https://www.archive.org/stream/cu31924028029035#page/n349/mode/2up/search/eagle
but Jennings imagined it a Saxon god. It’s interesting that the folklore is repeated in loads of places on the internet, but these days it’s more likely to be a Celtic god. That’s fashion for you? As a wildlife watcher, I’d rather prefer the easier explanation, that eagles like(d) to sit on the stone.