It's a GE GXSF39B00 that goes through all the motions, but the end result is that it has quit making soft water. It does not have a salt bridge.
There is always standing water in the brine tank, about 3/8ths of the way full. I manually cycled it and watched what it does. When I watched it, it added about 2" of water until the float valve made it stop. It never did suck up the brine water to recharge the beads. What needs to be replaced to fix this?