There is no perfect moment to jump in
You keep waiting for a natural pause that respects everyone, and it rarely comes cleanly. The good news is that a polite interruption is not rude if it is signaled clearly.
Signal before you speak
“Sorry to jump in — can I add something?” Naming the interruption out loud makes it feel considerate rather than abrupt, because you are asking rather than just talking over someone.
Keep it brief and hand it back
“Just a quick thought, then back to you.” Promising brevity is what makes people comfortable giving you the floor, and it holds you to actually being brief.