I ran another manual regeneration last night after removing some water
from the salt tank. As soon as I select the manual regeneration, I
see water moving into the smaller brinewell and my float valve starts
to rise. Then about 10 mins in the water level in the salt tank
starts to go up slightly. I didn't stay down there for the full
regeneration. But it does indeed look like its working. I also
bought some of those water test strips and it showed I had soft water
where it was supposed to be soft. I compared that to another area in
our upstairs that was not fitted for soft and it was definitely
hard.

So I think my mystery is solved. I guess my softener is just
extremely efficient with salt. It has an "efficiency" setting that is
on so maybe that is part of it.