Elevation -- the angle above the horizon -- is usually what's paired with azimuth.

Yes, the angle above the horizon is usually what is most useful because it is used to find something small but visible. In the case of my ascii moon, the angle below the horizon, is there to explain why something is not visible. The Moon is large enough that people can easily find it on their own if it is not obstructed by the Earth itself.

Consider the Moon as viewed from NYC at time of comment [0], it is hiding below the horizon. If you were to look at my website and then at the sky you might become upset that I am reporting the shape of the moon, but obviously it can't be seen. Hence why the website reports the angle below the horizon roughly half the time it isn't visible.

Adding Azimuth and Elevation when the Moon is above the horizon would be for completionism only and not the real enterprise use-cases served by ANSI compliant renderings of the Moon.

[0] https://aleyan.com/projects/ascii-side-of-the-moon/?lat=40.7...