You didn't mention if you have well or city water. Or the quality of the water.
I would tell most people that after 15 years, they have had the best of a water softener and it's time for a new one. Some folks like to repair the old ones, but in the long run, that just delays the inevitable and costs more overall.
Your softener is not drawing brine or it wouldn't be running over unless the clock died in mid refill. In which case it would continue to overflow until you bypassed it. The float devices in brine tanks don't normally last a long time, so I wouldn't put much faith in them.