Politely dealing with that team member who can't stop talking!

Though it's easy to share suggestion, it's really tough and needs practice and following multi-step approach to deal the situation.
Deal the situation in a meeting:
- It's difficult to interfere first: "Sorry to interrupt, you have a great/valuable points. Much appreciated for sharing. However, for the interest of time and/or current focus of the meeting, can we take this offline or we can schedule specific meeting to go in details, would that be ok. Appreciate your understanding"

For a repetitive situation, yes, you can use 1:1, or asking right questions back so that he realizes it (would you mind sharing why is this important, how does it impact, quantify, etc), or finally getting help from his/her management

All great points, but consider also looking in the mirror. Are you, in fact, giving them enough time and attention to make them feel valued when you don’t have a good reason for being in a rush? Are you over-loaded and treating everyone and everything like a transaction instead of a person? I’m certainly at-fault for doing this to my people when I feel overwhelmed.

All great points, but consider also looking in the mirror. Are you, in fact, giving them enough time and attention to make them feel valued when you don’t have a good reason for being in a rush? Are you over-loaded and treating everyone and everything like a transaction instead of a person? I’m certainly at-fault for doing this to my people when I feel overwhelmed.