I suppose you could consider Trickett sough to constitute a lower entrance, but as far as I know it's blocked before you get into the mine.
Seriously, there's only been the one entrance into the mine in modern times to the best of my knowledge. The main route through to the cartgate is still do-able and the pitch anchors are in good condition. I understand it is still possible to get into the lower levels but it's "interesting" down there....
Follow the horses, Johnny my laddie, follow the horses canny lad-oh!