At first I thought the bass just copied the rhythm guitar, but with a little volume, I was able to tell that wasn't the case. A few live videos (which had horrible phone camera sound quality, which conveniently butchers the bass) also had me convinced that something else was going on. From the few glimpses of Lucero's bassist, John Stubblefield, I was able to get, I realized a few things.
First off, he doesn't play it the same way every time. What am I supposed to do with that? How can I be playing it "right" if there's more than one way to do it? Is the way it's done on the record canonical? What about how it's done live? The important thing, I think, is to play a version that sounds good and supports the song. That might be eighth notes sometimes and other times it might be big fat whole notes.
Second, less can be more. In this live video, I noticed that a whole note filled up space while the rhythm guitar and drums drove the rhythm of the song. It's not always up to the bass to own that rhythm, especially when there's already a lot going on. Sometimes you just need big fat root notes to support the rest of the band.
Finally, I've learned I'm still pretty uncomfortable winging it. If I were to take one of the songs I was working on to a group of people to play, I feel like I need to have a more definitive answer for the rhythm than I do now. Either way, I do know that I want to start playing with other people ASAP.