At the beginning of your interview, you can say something like, “I like to budget myself for time during design interviews” or “I like to take time to think about each step when I can.” In addition to demonstrating effective communication skills, remarks like these convey that you are thoughtful as well. During the interview, you can also say, “I want to take a moment to think about this step.” Feel free to take 5-10 seconds, but note that after 15-20 seconds, the pause can become awkward. You can also verbally acknowledge that you are missing something but that you are going to move on to the next step to be conscious of time. If that point becomes relevant later, you can always circle back.
If you are brainstorming, be sure to let the interviewer know that you are in the brainstorming stage. That way, it won’t seem like your thought process is all over the place.