Hi Hilary,
Unless I’m misunderstanding your issue, in order to get animated randomness you need to select either Noise or Turbulence in the Random Mode setting, otherwise you just get one random value based on the seed. For the other modes you would need to animate the seed to have any change over time.
Edit: I forgot to mention that you could also animate any of the actual parameters (x, y, z position, for example) or the effector strength, but if you’re looking for automated randomness use Noise or Turbulence.