The guitar isn't plugged in, but the cable from the Axe-Fx III is still connected to a Morley ABC three-way splitter. The other 2 cables are connected to an FM3 and FM9. If I turn them off the ticking is still there, but if I unplug the cable from the Axe-Fx III, the noise goes away. Same result when I unplug from the splitter and plug my guitar straight into the Axe-Fx III; the ticking goes away. I'm going to assume there's either an issue with the splitter, or (ta da!) a cable.
Still kind of odd tho that it only happens with the 5 Sustainer types. Also, every now and then there is a dull THUD. I tried all of the other compressor types and there was no issue.