Silence is ok. You might need to let students know this. Sometimes the inner circle gets silent for a few seconds - that is ok and don't jump in as the teacher just yet. Sometimes you need to gather your thoughts by reading your notes or rephrase your inquiries. The Interaction Feedback Outer Circle will notice this; then that is your time to say it's ok.
You might need to let students know it is ok to build off others' comments and inquiries. This is part of the learning how to have a conversation. It isn't about one person saying one thing and then another person says something else unrelated. This takes getting used to doing - so, again, don't jump in as the teacher. The Interaction Feedback Outer Circle will point out these things and that can be your time to paraphrase and facilitate.
Some students won't talk right away or at all during a SC. I am ok with this. Not everyone is comfortable just yet. However, can you see the student still listening and participating through their facial expressions and body language? If you do, that's ok. Again, the Interaction Feedback Outer Circle might mention this, and you can facilitate this matter as needed. There are some teachers that set different requirements for this - like you get a point every time you talk - however, I don't like to impose this on the students because it is about them being in control of the discussion. Sometimes peers in the inner circle might ask the quiet person(s) to share, and usually that works.
I sometimes collect the students notes to see what they were thinking and noticing - because again, not all will talk or give feedback. I also like to copy student quotes and questions for future reference. :)
Overall, I find SCs the best way for my students to think deeper about artists and artworks, as well as their own personal art-making process. It has helped them think critically about the why and what they are communicating in their art.
Resources for more info on Socratic Circles. If you google, you will find a lot. This is the book (pic with link) I used during my school district SC training and several links below that are helpful.