Anup and Greg have pretty well covered everything going on here above, but to confirm:
What’s happening here is that the HDMI is running slightly too fast or slow compared to the Rossini Clock, so at some point the buffer in the Rossini DAC overflows/empties. HDMI is pretty notorious as a format for both short-term jitter and long-term absolute frequency accuracy - the likely cause of this issue.
When this happens, you drop or repeat an input sample - this will cause the DoP detector to trigger as PCM briefly, until it has had a number of “good” DoP markers to switch back to DSD. Switching between PCM and DSD will cause a mute, hence the ticks.
It doesn’t much matter how big the buffer is, once it runs out or overflows the loop will repeat at a rate that is proportional to the mismatch between clocks.
The Master Clock - in this case the Rossini Clock - has to be connected to every piece of equipment in the audio chain, otherwise as Anup has said you have two clock domains and issues like this are allowed to occur.
The crux here is unfortunately the GeerFab does not have any way to sync to an external Master Clock, so using this device you do need to use Audio Sync on the Rossini Player. That’s the only way to align the clock domains here, removing the clicks/pops.
With other PCM sources, if you have your system set up in the same way with the Rossini Player on Word Clock Sync but the sources not connected to the Rossini Clock, they will eventually display the same issue if left to their own devices for long enough. It may well take a fair bit of time (and changing tracks / channels etc. will reset the timer so to speak), and the clicks and pops may be much less frequent if the clocks are closer matched than with the HDMI source, but it will still happen. You may well be lucky enough that the clocks are naturally close enough that you can play an entire track without a dropout occurring, but from a purely technical standpoint the source and DAC (in this case Player) always need to be locked to the same clock source, whether Audio Sync or Word Clock if possible.