Judging by an old map, there were a few wells in the vicinity of Skirsgill (the house) which would be a mere step away from the stone. Though which one might be referred to here I don’t know. The site is right next to the river, just like Mayburgh (but now on the other side of the motorway).
PENRITH WELLS.
..Penrith was once noted, and has some fame still, for the number of its wells. The whole month of May was set apart for special observance of customs and ceremonies to be performed on each Sunday. There were four wells with a Sunday allocated for honouring each well. The Fontinalia opened at Skirsgill on the first Sunday; then in order Clifton, afterwards the well at the Giant’s Caves, supposed to be St. Ninian’s; and, lastly, at Dicky Bank, on the fellside, where the festivities were concluded.
From p42 of ‘Legendary Lore of the Holy Wells of England Including Rivers, Lakes, Fountains and Springs’, by Robert Charles Hope (1893). online at antipope.org/feorag/wells/
That sounds very similar to observations made by Stukeley when he was up that way, especially regarding the bits about the stones at Clifton, and the nearby well.