The nodal hands indicate the right ascension of the ascending and descending nodes of the Moon's orbit. These are the places at which the Moon's orbit crosses the Sun's orbit as seen from the center of Earth; there are always two such places, 180 degrees apart. When an eclipse occurs, both the Sun and the Moon must always be fairly close to one of the nodes.
If the Sun and Moon are very close to one another, the "eclipse needle" in the dial will rotate from its far left position, and will indicate the degree of eclipse at the location of the iPhone (or another location, if you've set a different location). If the needle reaches the first tick mark, the conditions are correct for a partial eclipse at the current location (unless the eclipse is below the horizon). If it reaches the second tick mark, the conditions indicate a total eclipse at the current location (again, unless the eclipse is below the horizon). The window in the eclipse dial will indicate what the current eclipse state is (none, "Partial Solar", "Annular Solar", "Total Solar", "Partial Lunar", "Total Lunar"). Note that for this purpose penumbral eclipses are ignored.
Note that the conditions for a solar eclipse are very sensitive to the location of the observer, and when there is a total solar eclipse it will only be visible in a small range of locations on the Earth. A lunar eclipse, on the other hand, is visible to the entire hemisphere where the Moon is above the horizon, though part of that hemisphere may be in twilight making the eclipse difficult to observe.
For example, there was
eclipse on Nov 13 2012 at about 22:11:48 UT
(it was centered in the southwestern Pacific; viewers in Australia and New Zealand
saw a partial eclipse but totality was visible only in a narrow band across the ocean).
If you set that time on the front of Geneva (make sure to use
the UT hand to set the time and make note of the UT +/- indicators
when setting the date),
the back side should look like this:
The Sun and Moon hands are aligned (this always happens every time there is a new moon), and they are both very close to the nodal hand Ω (in this case it is the ascending node, but either node could appear here).
As mentioned above, this eclipse wasn't at totality where most of Emerald Chronometer's customers are. But you can temporarily set a different location for Emerald Chronometer using the Settings panel, and then you can watch the eclipse needle move to "Total Eclipse". For this eclipse, at the time mentioned above, set the latitude to -39.95 (S) and the longitude to -161.33 (W), and at the time given above the eclipse needle will look like the image at the right.
For a lunar eclipse, the situation is slightly different. For example, there was a total lunar eclipse on 2010 Dec 21 at about 08:16:57 UT and it was most visible in longitudes aligned with the western United States. Setting that time on the front of Geneva (again being careful to set the UT time and date properly) should result in the back side appearing as shown to the left and right. Note that neither the Sun nor the Moon are exactly aligned with the nodal points, but they're close and they are exactly 180 degrees apart (as they are on every full moon).
If the Moon is above the horizon at your location at this time, you can see the eclipse needle move on Geneva without changing the location used in Emerald Chronometer. At the time indicated above, the eclipse needle will look like the image on the right.
You can use this same technique with historical eclipses, moving the date and century hands on the front of Geneva to match the dates of known eclipses, such as this NASA list of historical solar eclipses, this list of upcoming solar eclipses, or this list of upcoming lunar eclipses. Take care to set the dates correctly, especially with BCE dates where dates on the front of Geneva are read counter-clockwise from 12 o'clock.
Here are some upcoming solar and lunar eclipses, with optimum locations marked for solar eclipses:
You can also use the "next moon phase" pusher to position the Moon; it will stop where the ecliptic longitudes of the Sun and Moon are identical or are off by 90, 180, or 270 degrees. This pusher is available when the crown is pulled, and is at the lower left of the watch case when viewing the back. You can go backwards by phases if you first tap the forward/reverse switch below 6 oclock; it will turn red to indicate reverse.
The new-moon and full-moon points aren't exactly the points of maximum eclipse, however; once you are at a phase point, you can then move the sidereal minute hand back and forth, watching the eclipse needle, to see where the needle reaches its maximum. Then at that peak you can read the eclipse window to see what kind of eclipse, if any, will be visible at this location.
The Sun and Moon hands can be surprisingly far away from the nodal hands and still have an eclipse be possible. The angle between the Moon's orbit and the Sun's is quite small (about 5 degrees), so the Moon can be a fair distance from the node in right ascension (RA) (perhaps as much as 10 degrees) and still be sufficiently close in ecliptic latitude to result in a partial eclipse.
On the other hand, just because the nodal point is close doesn't mean that an eclipse is guaranteed, as mentioned earlier. Use the eclipse needle for more precise results, and please don't plan your once-in-a-lifetime photograph solely on the data presented in Emerald Chronometer; there are better tools for that on the web (you can start at the NASA sites linked above).