I solved the mystery
The voltage fluctuations seem to occur when the battery goes through a temperature change. The first time it happened was when I brought the battery in the house (+ 20 degrees) so I wouldn't have to go out in the garage to obsess over it. It happened again last night when I closed the garage door (+10 degrees). Other than that, it seems to have stabilized out to 12.5V with a loss (so far) of about .01V per day. I'm still going to get a hydrometer and check the gravities, but I'm pretty sure I'll be able to declare it a good battery, at least until I put a load on it.
The voltage fluctuations seem to occur when the battery goes through a temperature change. The first time it happened was when I brought the battery in the house (+ 20 degrees) so I wouldn't have to go out in the garage to obsess over it. It happened again last night when I closed the garage door (+10 degrees). Other than that, it seems to have stabilized out to 12.5V with a loss (so far) of about .01V per day. I'm still going to get a hydrometer and check the gravities, but I'm pretty sure I'll be able to declare it a good battery, at least until I put a load on it.