Is there an idiom for someone who nods and listens usefully?

I had a coworker who would occasionally say something like, "I can't solve this problem. Would you play Wooden Indian for me?" (referring to the carved figures that used to stand outside cigar stores) His meaning was: I need to talk through this with a live person who will listen and ask appropriate questions, and I think I could see the solution myself at that point.

I often need this, too, as I process problems best aloud; but I don't want to run around asking coworkers to be "wooden Indians" as this seems racially insensitive. Is there another idiom for this role?

In software engineering, a person that agrees to listen for no purpose other than to allow a problem to be expressed verbally is commonly referred to as a "rubber duck" or "rubber ducky".

https://en.wikipedia.org/wiki/Rubber_duck_debugging

I’ll often tell a colleague “Hey {name}, I need a sounding board” or “Hey, {name}, let me bounce this off you”.

Merriam-Webster (1c) defines sounding board as “a person or group on whom one tries out an idea or opinion as a means of evaluating it”, but the actual usage in this context is more accurately described by Urban Dictionary - “A sounding board is a good listener, and either confirms what they hear or offers an opinion when [what] they hear is "off key".”.

Bouncing an idea off ... has been the subject of a question here on ELU, and was answered well. Oxford simply defines it as “Share an idea with (someone) in order to refine it.”

Both usages should be considered informal/colloquial, just as are “wooden Indian”, “rubber duck”, and “nodding dog” mentioned in this question and its various answers.

A third phrase that I’ll occasionally use, in a semi-humorous vein, is semantically equivalent to either of the above: “Hey, {name}, I need a sanity check”. Strictly speaking, a request for a sanity check (see Wikipedia) is simply asking whether there is any obvious problem with the idea/code, but the actual usage tends to be closer to that of the other two phrases.

Our office used to call this the "nodding dog syndrome" after the toy once found in a lot of British cars.

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The advantage is that they do NOT ask questions that can derail your thoughts, but will always nod approvingly, encouraging you to keep talking.

While you might have to explain what you want to someone the first time you use this phrase it is clear you are asking them to perform a certain role not just engage in a standard discussion.

You need someone to listen to you thinking aloud, which basically means that you do all the thinking and talking and the other is just creating an environment where thinking aloud can be done more comfortably.