Ok, I looked a little closer at the UVLO feature and I'm a little confused. The datasheet says there are two thresholds: the "UV turn ON" (12V) and "UV turn OFF" (10V). Here's what I think it means. The VCC needs to rise above 12V initially to turn on the device. After that, if it drops below 10V, it will turn off the device. Am I correct?
As a test, I stacked a single AA battery on top of my 12V supply to get about 13.5V. I put that on the VCC pin and suddenly the LVG pin went high. So that seems to confirm my theory.