The mirror pool must be near the shrines at the bottom of Mt Haguro -
The bridge mentioned in the programme (being repainted!) -

The top pool at Mt Haguro in July 2006 - I thought this was the mirror pool? It is called "Kagami" (mirror). Because women were forbidden on Haguro centuries ago, they could not have thrown the mirror into the pool themselves. Checked here - the pool is at the top. So what's going on with the British Museum information?

To climb to the top of Haguro, there are now 2246 stone steps -