Hi Kevin,
It looked like a hot pixel problem to me because we see a continuous series of max-duration corrections on both RA and Dec and the guide star staying at a fixed offset from the lock position - RA (blue) and dec (red) star offset is not changing despite the guide pulses being sent. The up and down wiggles are probably due to camera noise, with the hot pixel being fairly dim.
The star selection function in PHD2 is usually pretty good at selecting stars over hot pixels. There is a convolution function that usually all but eliminates the hot pixels from consideration. However, if there are no stars in the field then a hot pixel is the most likely thing to be chosen. If it ever happens again, you can do File => Save image to get if raw FITS image from the camera so we can analyze the image to make sure phd2 was not incorrectly choosing a hot pixel over a guide star.
The debug log does record lots of information about the Auto-find. In the instance around 00:31 there were apparently only two good candidates, SNR 61.1 and 87.7, but those were rejected because they were too close together (about 8.6 pixels):
00:31:05.783 00.001 7152 AutoFind: too close [362, 284] 61.1 - [355, 289] 87.7
Your large search region setting (50) makes it more likely for phd2 to reject stars as being too close, but those stars would have been too close even with the default search region (15). The threshold for "too close" is (search region + 5 pixels).
Based on your focal length in the log, I'm assuming you are using OAG. This is the big down-side of OAG. If your target is in a sparse area of the sky (galaxy season), you may need to make sure that there is a good star to guide on rather than trusting that one will be found automatically. You may need to specifically frame your target to get a guide star in the guider FOV, or else rotate your OAG to find a star.
Andy