I don't agree with throwing someone's mistakes in their face. All of us dislike that and feel defensive right away. On the other hand, I do think that if you love someone and see something they are doing that is destructive either to themselves or their relationships with others, it takes a lot more love and courage to bring it up than to let it go and leave the other person to learn the hard way or not learn at all. I would wish for someone to care enough to do that for me in return.
An example of this might be an over-enthusiastic hockey parent who is putting enormous amounts of pressure on their child which is damaging the relationship. If their spouse (gently) attempts to make the STJ person aware of what effect their behaviour is having, is it likely to be resented (don't make me feel like a bad person because I know I'm not!) and ignored, or considered?
You also were saying you need an example of a situation where the STJ needs to show more vulnerability than being in the role of being needed to give help or advice. An example might be if someone brings up the fact that something the STJ said that day hurt them because... Would the STJ be able to step out of the role of telling the other person what to do and see it as a problem to be solved together (this is more vulnerable, than giving advice because it implies action needed on both people's parts and therefore discussion and some kind of resolution, which may or may result in having your own way)? Or would it boil down to the STJ deciding that one or the other will need to just deal with it in some way on their own (either get over it for the one person because the STJ knows it's not a valid worry or the STJ resolves to change their behaviour - w/o further discussion)