Brine Refill Problem ( little or no water )

Does the tank float have to touch the bottom of the tank to signal the autotrol to put water into the brine tank

* No.

or is it metered after the brine is injected into the softener ( I'm wondering if the float is in the wrong position)

* Float is to prevent OVERFLOWING, and does not control refill.

Refill is a "timed" cycle ( at the end of the regeneration process ),

AND

The "flow" rate of this timed refill is controlled by the Brine Control Dial.

This sometimes gets clogged and requires cleaning ( it unscrews from the Valve Body ). * Also, note:

There is one of your two flow control balls ( 4F ) sitting inside behind it ( refer to parts diagram of the valve body ).

And unscrewing is all there is to removing the control from the valve body.

And once removed you will see if there is any debris blocking the small white teeth openings ( they are what "regulate" the amount of water that get past during REFILL Cycle ).

SEE: BRINE CONTROL DIAL 3-19 lbs. 1F-19 or 1034263

OR
for LOGIX controller Valves,

Old ( obsolete ) style Brine Refill

New style Brine Refill

And this video shows How To Depressurize the Autotrol Valves.