It could be part of the flow meter that tells the softener when enough water has passed through to need regeneration. Not sure where it goes but there should be some kind of housing and hook up for it. I have a Whirlpool softener and if I run my water slowly it pulses implying that the turbine could be on the discharge side, but only guessing.
Glad you figured it out, since I was going to say mine (not Whirlpool) goes on the intake. There should be a small electric sensor that picks up the rotation of a little magnet in the turbine. Before I installed a whole house filter I had to take mine out every now and again to clean it.
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