NavList:

Your problem with figuring out how to calibrate a Bris Sextant (BS) using an Artificial Horizon (AH) arises from the fact that a BS was never intended to be used with an AH.

The BS is held near your eye and looking toward the sun and horizon in that direction, you see multiple suns arrayed verticaly above and below the horizon.  The top sun is the direct image at an altitude, Hs, given in the almanac for the time of observation, the lower suns are at altitudes Ho = Hs - mxA - nxB.  A and B are angles determined by non parallelism of the Bris plates.  It is calibrated by observing the time when the various sun images rest on or under the horizon.

The important feature is that the horizon is the indicator.  An AH eliminates that pointer.  If not near a far horizon you need to use dip short horizon and correct for the error.

DaveF