It turns out that there's no relationship to the eclipse, but rather to the time of the year.
Pretty much, the horns of the crescent coincide with the north and south poles of the Moon, so the waxing crescent pretty much illuminates the "right" side of the Moon (what we call the western limb when viewed from earth), and is centered pretty much on the orbital path of the Moon, and the Moon's equator (not quite, because the Moon's orbit is not quite on the ecliptic). But the illuminated portion of the waxing crescent will appear to be nearer the "bottom" of the Moon as it sets, near the right side of the Moon as it crosses your meridian, and near the "top" of the rising Moon. See the screen shots from http://stellarium.org below:
The Waxing Crescent Moon setting on 1/29/09 (note that the ecliptic is making a fairly steep angle with the western horizon, and that the Moon is north of the ecliptic. The north pole of the Moon is on the "right" side of the moon here, and the Moon's equator is almost vertical:
This was the Moon at meridian crossing on 1/29/09. View is to the south, of course. You could have seen it naked eye if you looked in the right place (you can see Venus naked eye, too!) Notice that the illuminated crescent is pretty much on the right (western limb) side.
Here's the Moon rising on the morning 1/29/09. Notice that the illuminated portion of the Moon is kind of "on top", but that the angle the ecliptic makes with the horizon is less steep than the angle it makes at sunset, so the crescent is not quite as "on top" as it was "on the bottom" when it set.
The places where the celestial equator (blue) and the ecliptic (red) cross are the equinoxes, and the equinox in these images is the vernal (spring) equinox. When the vernal equinox is setting, the angle between the ecliptic and the western horizon is large (the ecliptic is more nearly vertical). When the sun is near the vernal equinox (March and April), the angle between the ecliptic and the horizon at sunset is at its greatest, and Venus and Mercury, if they're east of the Sun (and therefore setting after it), will be high in the sky right after sunset.
Similarly, in September and October as the autumnal equinox rises, the angle between the ecliptic and the eastern horizon at sunrise is the greatest, and around the autumnal equinox Venus and Mercury, if they're west of the Sun (and therefore rising before it), will be high in the sky and well placed for viewing.
The following screen shots show, in order, the rising vernal equinox, the setting vernal equinox, the rising autumnal equinox, and the setting autumnal equinox.
Rising Vernal Equinox (low angle ecliptic)
Setting Vernal Equinox (high angle ecliptic)
Rising Autumnal Equinox (high angle ecliptic)
Setting Autumnal Equinox (low angle ecliptic)
You should also note that the celestial equator makes an angle with the horizon of (90-latitude) (I have Stellarium set to White Plains, NY at 41N), and it remains constant throughout the year.
If you've never imagined it, think of the ecliptic wobbling across the sky each day. And if you can't imagine it, run Stellarium at high speed, and watch it.
Now, back to my friend's question! Eclipses occur as the Moon crosses the ecliptic on its way north or south (called the "nodes" of the Moon's orbit). That's why solar and lunar eclipses come in pairs about 2 weeks apart (a lunar at one node, and a solar at the other), and the eclipse pairs occur every six months or so when the nodes line up with the Sun! The nodes drift with respect to the sun, but in recent years the eclipses have been occurring in the winter and summer. Winter waxing crescents, for the reasons described above, tend to look like they're lit on the "bottom" But watch the crescent moon after the July 22, 2009 solar eclipse....it'll look like this:
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