I finally managed a couple of shots (see below), at least to serve as a record.
Although Sweetgum isn't native to California (it's planted as an ornamental), I've read that it's a favorite sapsucker food source. I was looking at the holes and noticed the sap was actively running (see amber-colored spots in next photo).
A sapsucker spends a lot of time excavating and maintaining these sap sources. And sapsuckers are "specialized for sipping sap," with brush-like tongues (Walters et al. 2002). Once made available by the sapsucker, this sugary fluid is also visited by other birds, insects, and mammals.
When I looked out the window the next time, a small bird was flitting around the trunk where the sapsucker had been working. I thought it was a chickadee at first, but then realized it was a hummingbird hovering near the sap wells. (Apparently, some hummingbirds are so interested in this sap resource that they'll make their nests near "sapsucker trees" and they'll follow sapsuckers during the day.)
It was raining and very dark under the dense tree canopy, but I decided to try again. I went out and "hid" by a nearby tree trunk. The sapsucker was too wary, but the hummingbird returned and I got lucky with this shot (I think it's a female Anna's Hummingbird):
You may have noticed that I haven't identified the species of sapsucker. I think it might be a Red-breasted Sapsucker (Sphyrapicus ruber). However, there seems to be more black on the back of the head than I'd expect, so I also wondered if it could be a hybrid Red-breasted Sapsucker x Red-naped Sapsucker. If you have any thoughts about this, I'd love feedback about this bird's identity.
If you're interested in trying to figure this out, I've included a couple more views (below).