Very little would be needed, as 5E already does a decent job for dungeon crawls. Primarily it should consolidate the damn rules! The rules needed are scattered all over the DMG and PHB, which is why most people feel they don't exist. Darkvision isn't as much of a problem when you realize that -5 on your Passive Perception and disadvantage on Perception checks means you're likely going to miss all the traps and secret doors, plus you'll get ambushed more frequently. Light being a cantrip is only an issue because the Cleric has so few useful cantrips, but adding Concentration would probably make it a non-factor.
The biggest actual change would be in how to use Passive Perception/Investigation. If you simply compare flat numbers, as JC claims, the mechanic just doesn't work. Either the party is going to succeed or fail from the moment the adventure begins, barring them getting advantage or disadvantage. Currently 1D&D is requiring actions for checks, meaning Passive skills are going away, and I feel that's probably the way to go. If they keep Passive for secret checks, I'd recommend using the Mike Mearls method (which I currently use) of having the trap/door/whatever make the roll against the Passive score.
Travel activities need a change and made meaningful. Making a map is easy and either has no benefit or completely negates the navigation activity. I'd also separate watching for danger into looking for enemies and looking for traps/secret doors.
Time needs to be more easily tracked. The current setup is fine, but a suggestion to consolidate it into manageable segments would be good. I use 1 minute increments for a lot of nuance, but 5 minutes and 10 minutes would also work well. This plays into the time for resting and wandering monsters, which needs to be better address. Putting the environments with the monsters would be helpful in this regard, along with the full lists.
Other than that, I don't think they need to do that much to make 5E work great for dungeon crawls. The real issue with getting D&D "back to the dungeon" is that players don't really want that as much anymore. Having an occasional dungeon crawl is fine, but there's a reason DM's like the 5 room dungeon concept. I personally love dungeon crawls, but my group is kinda meh about them.