I've found the passage.
"Employing the most recent measures for Vega’s proper motion into the long-term calculations for its motion in the sky, we see that Vega achieved its highest declination of 86.54 degrees around 12,070 BCE.
Vega matched the subterranean passage not simply at some passing date, but exactly when the star was at its northern culmination, the closest it comes to the celestial pole in its twenty-six-thousand-year precession cycle.
In addition, the precision with which Vega seems to have matched the center of the shaft is surprising.
Given the height and length of the shaft, its viewing angle actually includes a range of declination angles from 86.22 degrees to 86.87 degrees, centered on 86.54 degrees, and Vega appears to have hit it directly in the middle, exactly at culmination.
Therefore, if these calculations and measures for Vega prove to be accurate, Vega began shining down to the bottom of the subterranean passage around 12,320 BCE, when Vega’s declination rose above 86.22 degrees, and around 12,070 BCE, Vega shone down the center of the shaft until ca. 11,820 BCE, when Vega sank below 86.22 degrees declination again and no longer shone to the bottom of the shaft."
If the calculations are correct, Vega shone down the Subterranean Passage for a period of approx. 500 years.