Early autoland systems did not have rollout capability, which limited the original CAT III ops in the US to an RVR of 700 feet. Once rollout guidance was implemented, CAT IIIB minimums were approved. Since that time, there has been some finessing of the requirements, and current US requirements limit CAT III operations without rollout control to 600 RVR. Because of this softening of RVR requirements, the traditional definitions of CAT IIIA and IIIB have little value anymore...what really matters is whether the aircraft is fail-passive or fail-operational, and whether it has functioning rollout guidance.
Your MEL may provide some insight on this. For example, with respect to the 757/767, it is possible to defer the rudder pedal nosewheel steering. However, if you do this, you should be restricted to at least 600 RVR because the rudder pedal steering is how the autoflight system tracks the centerline. No rudder pedal steering, no rollout guidance.
With that in mind, if the localizer signal is unusable during some portion of the rollout, the runway should be restricted to at least 600 RVR.