Instead of captain, I'm going to liken the spot of caller to the party's communications officer. If this were a Vietnam War movie, the caller would be the soldier with the telephone backpack calling in to headquarters during a battle.
The caller's primary goal—the entire purpose of there even being a caller position in the first place—is to move the fun and action forward. To go from "talking" to "doing." The caller does so by quickly and concisely relaying the party's actions to the GM.
"Quickly," meaning promptly. For example, if the party comes to a door, the caller should immediately (no prompt needed) say, "Thief listens at the door. If he hears nothing, Fighter tests it. If it's stuck, Fighter kicks it down. We're all standing in formation, ready for combat."
A door is routine. The caller should already know the party's actions from several past examples. There's no need to ask anyone what they do, because we've already done this many times. The caller is stating the obvious—not making "command decisions."
As for picking the correct path, that should fall under the routine as well, or it should have been previously discussed, perhaps with the party's mapper. If there's truly a fork in the path with no significant difference, then the caller simply picks one or the other; not because he or she is "in charge," but because discussion would only slow down play.
In regard to special challenges like a symbol puzzle (or whatever), the caller should quickly "pass the conch" to the appropriate player of a character who's best suited for the job. The best callers are those who help the DM make certain everyone gets a chance for as much time in the spotlight as possible.
Once a good "standard operating procedure" is established in a session (often during the phase where marching order is determined), that should take care of most common dungeon situations. If a caller thinks the party should take special care ("We look up at the ceiling for giant spiders"), then by all means tell the GM, but any player can voice such concerns.
From one caller to another, it's a numbers game: the more rooms the players toss, the more treasure they'll find, and that's our entire goal in the game: get treasure.
A good caller knows the difference between minutia and what's critically important to the players' survival. Discuss only the latter, and even that should be brief. Make your plan without over-analyzing the situation (often resulting in "analysis paralysis"), then execute it without second guessing yourselves in the middle of doing so.
The best callers do all of that with one thing in mind: move the fun and action forward as quickly as possible. Let's not just talk about it; let's do it!
All this talk about the caller not being the party leader by default isn't to say that the caller should't strive to be such! The best callers are good leaders!
However, the best leaders do not have to be the caller!
"Leader" is a social position, not a delegated power.
Here's bonus tip from one caller to another: sometimes, the dungeon is set out like a puzzle—but the pieces are spaced far apart. Don't spend too much time on one piece. Sure, give it a good once-over, but be quick to move on and leave it for later. More often than not, later in the dungeon, it becomes apparent where that piece fits in the puzzle.
For example, the classic stone statue missing a head. You can search it up and down, pull all its fingers, set a freshly-disembodied orc head atop its shoulders—do ALL the THINGS—and never figure out why its there. In fact, it may not even have a reason! Maybe it is just junk! Then, down on the next level, you find a statue's head. Now you know where it goes, but there's no way you could have "solved" the "puzzle" earlier.
The name of this blog is Blood or Treasure. That's the metric by which I weigh every decision I make as caller: risk or reward?
As a caller, I found myself asking, "Blood or treasure? Will this course of action ultimately result in chance of harm (blood)—which I do not seek—or will it lead, directly or indirectly, to treasure?"
Of course, everyone knows that sometimes we will have to fight or face danger to win our treasure. In that case, the answer to the question, "Blood or treasure," is "Both."
That, dear readers, is the best answer!