Various tidbits of table management, in no particular order.
Structuring exploration into rounds of some length is probably a good idea.
Specifically asking each player for their input personally, rather than waiting for them to speak up and interrupt, is another trick - very easy if you are using a turn structure, as you ask what each person wants to do.
Run a physical timer, if you need, so that nobody takes up more than a couple minutes in real-time at a shot. You'll probably find two or three minutes is a long time for people to talk.
When someone hogs the spotlight for a bit, announce, "Okay, now the scene switches over here to the other characters, to see what they are doing."
When you ask what they want to do, ask, "What do you want to accomplish?" Do this a few times over, and they should learn that they ought to name the goal, and suggest a path, "I want to see if I can remember anything relevant about such carvings - will Arcana do it?"
If they cannot think of what they want to do, ask them what they want to know more about. Find a way to get them a bit that might suggest an action.
When some folks end up sitting around, because there really doesn't seem to be much for them to engage with, change it up - throw some kobolds or ninjas or whatever is appropriate to change up what the scene is about for a while.
Or, when some folks end up sitting around, do a quick summary of the exploration, and move to the next scene. Rather than do a detail on each. and. every. sarcophagus. you summarize - "You go over all the sarcophagi, and overall, you find X, Y, and Z. Nothing bites your hear off."
When you are constructing your scenario, make sure your design already includes stuff that is relevant to the skills across many party members. If you are using a published work, and it doesn't seem to have that, then add stuff.
Remember some notions of character motivations. One reason for a scene to play out like you described is that some characters really did not want to muck with the dead, but the rogue insisted. The players, however, may not want to start a confrontation, and will then let the one character continue what they are doing, even though the characters might not.
Structuring exploration into rounds of some length is probably a good idea.
Specifically asking each player for their input personally, rather than waiting for them to speak up and interrupt, is another trick - very easy if you are using a turn structure, as you ask what each person wants to do.
Run a physical timer, if you need, so that nobody takes up more than a couple minutes in real-time at a shot. You'll probably find two or three minutes is a long time for people to talk.
When someone hogs the spotlight for a bit, announce, "Okay, now the scene switches over here to the other characters, to see what they are doing."
When you ask what they want to do, ask, "What do you want to accomplish?" Do this a few times over, and they should learn that they ought to name the goal, and suggest a path, "I want to see if I can remember anything relevant about such carvings - will Arcana do it?"
If they cannot think of what they want to do, ask them what they want to know more about. Find a way to get them a bit that might suggest an action.
When some folks end up sitting around, because there really doesn't seem to be much for them to engage with, change it up - throw some kobolds or ninjas or whatever is appropriate to change up what the scene is about for a while.
Or, when some folks end up sitting around, do a quick summary of the exploration, and move to the next scene. Rather than do a detail on each. and. every. sarcophagus. you summarize - "You go over all the sarcophagi, and overall, you find X, Y, and Z. Nothing bites your hear off."
When you are constructing your scenario, make sure your design already includes stuff that is relevant to the skills across many party members. If you are using a published work, and it doesn't seem to have that, then add stuff.
Remember some notions of character motivations. One reason for a scene to play out like you described is that some characters really did not want to muck with the dead, but the rogue insisted. The players, however, may not want to start a confrontation, and will then let the one character continue what they are doing, even though the characters might not.