Usually the only time I'm actually helpful in situations like that is if I have esoteric knowledge or experience that is uncommon and directly related to the problem at hand - "Oh, I ran into this 3 years ago, here's what we did to solve it". Your peers have already tried the obvious things.
Another rule of thumb to notice when this is happening is the word just. "Why don't you just..." is a belittling thing to say, as if they hadn't already thought of the obvious. Better is "why didn't X work"?
For instance, I don't see a good reason why having consciousness of X is in any way fundamentally different, than having an ability to play StarCraft at MMR Y this instant in time. IMHO, conceptually they are the same and the only difference is the game being measured.
Actually, now that I think about this, I'd extend it to just about everyone, not just academics/engineers/etc. Imagine two people working on a plumbing problem. An hour into it, Bob waltzes in, looks at it, and says, "did you try __?" The two people who have actually been working on it roll their eyes and mutter, "yes, Bob, we've been working on it."
Sometimes Bob will get lucky and notice something they didn't, because they're too deep in the weeds, but I think people dramatically overestimate how likely this is.