The noise came back again today, so I tried plugging the guitar straight into the audio interface. I got the same clicking there, so I could exclude any errors to the POD itself :) I then decided to check with all neighbouring apartments to see if they were using some powerful electronics, or also had issues with clicking. The guy living below me also had an electric guitar, and he got the exact same noise with his guitar and amp. The guy on the other side of the wall didn't notice anything himself, but he told me that he had been talking to a neighbouring lady who often got some noise in her hearing aid. He said that it always occured to her whenever the robotic lawn mower on our yard was going. I then decided to speak to the janitor of our community and ask about the lawn mower, and he could confirm that a lady had the same noise that I described. I then asked him to turn it off so I could see if it would cancel the noise for me, and it did!
I would never expect that, but I'm very glad that I finally found the cause ^^
The janitor also said that the lawn mower parks in it's charging station at 6pm every day,
so I'll have to wait until then before recording :P
Philipozz's post in Clicking noise on my POD HD500X was marked as the answer