So, to answer my own question, I initially thought I had checked the obvious fuses in the fuse panel under the backseat. However, I revisited them this morning and discovered a fuse labeled “acc.” It’s a 10-amp fuse that appears to control the “key on” side of the busbar. Replacing the fuse resolved the issue.
Now, I’m curious if it would be safe to replace that 10-amp fuse with a 15-amp fuse. I’ve only connected LED lights to the busbar, and I can use all four sets simultaneously without blowing the 15-amp fuse.