NavList:

That's included along the line of sight.  In the diagram, instead of "body 1" and "body 2", you can substitute "body" and "horizon".  The center of the sight line is right at the junction between two mirrors in the stack(s), so one half of the pupil is looking in one direction and the other half the other.

By the way, I misspoke slightly about the "double reflection".  As it turns out, just the first mirror block is already "double reflection", in the sense of keeping horizon and object together under small rotations of the whole instrument.  No additional mirror or mirror block is needed for that, although additional blocks are needed to increase the set of available angles.  For example, three blocks might be a good tradeoff---no problem that three is not a multiple of 2, and 10^3 angles might be okay for usability.

The surfaces are all opaque mirrors, so the optical path doesn't go through the glass blocks, as it would with a conventional sextant with split horizon mirror.  With Greg Rudzinski's suggestion of prisms, though, there would be some glass in the path, but optical glass is quite good and a few centimeters would not hurt image quality, especially at these low magnifications.

I did put a few small mirrors on a wooden frame to try it out over the weekend, and it seems to work as expected, but I have a bunch of small "craft mirrors" arriving in a day or so, so I can make a better prototype.  The plan is to 3D print some plastic blocks with the angles built in, dice up the mirrors, then affix mirror strips along the various edges.  (These are second-surface mirrors, so not ideal, but good enough to start with.)  (Also, the plastic will not be stable, nor the angles all that accurate; this is just to try out the assembly for usability.)

Cheers,

Peter