I just want to be sure I am visualizing this correctly, because it seems odd. The Moon is tidally locked to the Earth but there are wobbles to its motion due to libration. So from a point on the surface of the near side of the Moon, the Earth would always be near the same place in the sky? It would describe a small circle or a side-to-side wobble over the course of a month, but never move far from that point?

That would seem very strange, like it was a gigantic stage prop or something. We are so conditioned that everything rises and sets (except for a few stars near the poles). 

Still new at stellarium but here are some quick capture gif  lasting one month. Sorry about the quality- limited to 256 colors for smaller gifs. Date on lower left corner. By the way the sun is of course the brightest and i use it as reference for recording (start record when sun is in frame then stop when it appears again in the same position which is roughly one month)

Location on Moon : Sea of Tranquility

You are looking straight up

Yellow lines are azimuth



second picture:

Zoomed view of earth

One whole day 24 hours (give or take a few minutes)

Location on Moon: Sea of Tranquility

You are looking straight up

Yellow lines are azimuth (gif itself rotated to approximately match the orientation of the 260 degree azimuth line in the first picture)



Answer for Emilio Pisanty comment on whether the oscillation is detectable by eye

stellarium

Field of view 60 degrees (default view when stellarium first opened)

Picture 3

Shows one end of the oscillation near the 200 azimuth line (see yellow arrows)

other end of ellipse near 185 azimuth line

you can use Gemini (lower right corner) for reference (see yellow arrows) from head to crotch of one Gemini twin would be a good reference for how wide the oscillation is (not sure if your sundial can detect the difference)



picture 4

shows other end of the oscilation near the 185 azimuth line (see yellow arrows)



picture 5 shows my stellarium location settings on the moon


