I did a little more investigation tonight, and here's what I'm seeing:
I unplugged the ARINC module and powered up the SkyView system multiple times. Each time, all modules were present and working correctly.
I then plugged the ARINC module back in and powered up the SkyView system several times. Most of the time, all modules other than the ARINC module appeared on the network, but the behavior of the ARINC module was still inconsistent. On one try, all devices appeared as online when I accessed the network status page, but the light on the ARINC module was off. On another try, the ARINC module appeared as offline, but the light was on solid. On yet another try, all devices showed as online and the ARINC light was blinking fast, but when I entered a flight plan on the GTN, the SkyView HSI didn't show the course. I checked the light on the ARINC module and it was now off. A couple of times, all devices showed as offline, but I only saw this happen when the ARINC module was connected to the network
I also wanted to see if I could determine why I was getting so much audio clicking. If I connected the audio lines to either display separately, I didn't get any clicking. It appears to only happen if both displays are connected together.