I headed to San Joaquin Marsh after Don and Rick refound the Red-throated Pipit, but missed it by about 5 minutes. After about 40 minutes, Victoria (don't know her last name) refound the target bird. It was only there for a few seconds once she showed it to Lee Bush and me and then it seemingly disappeared again when the flock flew, and did not reappear while I was there for the next 10-15 minutes. A couple tips:
At the time of day that I was there (late morning heading into midday) the best vantage point was easily the little dirt path going along the cinder block wall, on the eastern side of Pond C in the northeast corner. At least in my case, this puts you generally closer to the birds than if you are standing over in the crook of the L shape of the pond. I tried both and found the eastern dirt path to be a much better angle.
The easiest way to tell the bird is probably going to be to look for its back. The American Pipits all have uniformly gray-brown backs with black stripes. The Red-throated Pipit has conspicuously whitish stripes on its back. It also has fine black streaking on its cap. From the front the birds look superficially very similar.
I have uploaded some photos online that should help show the difference. I wasn't thinking much about a comparison and only took one American Pipit photo just to check my camera settings, but you can still very much see the differences.