OK. But if you just connect in mono (guitar -> input 1 -> output 1 -> amp), the noise is gone?

No, my initial assessment was incorrect. The noise is present in both stereo and mono configurations, and on both the wet and dry signal.

I also switched power adapters with my Space pedal to see if it might be a power issue. The TimeFactor was still clicking. The Space is clean.

I ran a direct signal into my audio interface too, and the clicks are present. I gave the inputs and outputs a cleaning with deoxit, but that hasn’t changed it.