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Steve, have a look at the Sun's SHA on that date. One way to do this is to check the USNO web app that we've been discussing. Start here: https://aa.usno.navy.mil/data/docs/celnavtable.php. Then enter time and location date to end up here. Though this tool does not directly display the Sun's SHA, you can easily calculate it: SHA* = GHA* - GHAaries. This approach based on SHA works well on the equinoxes and the solstices, too. On the equinoxes, since the Sun is moving rapidly in Dec, you can also check to see when the Sun's Dec changes from its hemisphere North/South. The times may not exactly match due to a couple of minor issues, but they will be close.

Frank Reed