Firstly, congratulations on your phone interviews. Even getting to that step is a huge achievement with the number of job applicants to any particular position.
Second, it sounds like you need to relax and have more confidence. As you said, most pauses over the phone are so the interviewer can take down your information. Without body language cues, it can be hard to determine this; but just trust in the fact that 99% of the time this is what is happening. The same goes for the interviewer though - they can't see your body language to tell how confident you are. They can only hear your voice, so it's important you sound as confident and calm as possible!
Next, practice the questions you think they will ask you. Practice giving your answers in a concise way. Since it's a phone interview, you can even make notecards to have on hand so you don't forget any information. That way, when you do answer a question and are finished talking, you won't feel tempted to keep on talking when there is silence as you will know you have answered the question fully.