Four lesser options, one major one.
Fast-forward the split party part. Don't dwell on stuff as much as you otherwise would.
Snack and bathroom break time. Shoo the other players off. This will serve as a cue to the sneakers that they should include everyone eventually.
Metagame, encourage the group to find ways to include people even when it's suboptimal.
Spring stuff on the other party to keep them occupied. Sure, if they just get a lead, they can wait to follow up, so make the action come to the PCs - someone kicks down the door or otherwise looks to interact with them NOW.
Give them all equal spotlight time. 5 minutes dealing with sneakers or interrogators, 5 with the others. They'll either start going to do stuff of their own accord, or they will, heaven forfend, roleplay with each other.
Number 5 is really my favorite. We've had plenty of great moments while half the party is doing something "important" and the other half goes to a bar and gets in trouble. All you have to do is give them the spotlight time, PCs are notoriously twitchy and impatient and will find ways to entertain themselves, "on task" or not.
My added thoughts based on your question edit.
You don't need to balance "in game" time. If one group went and did something for six hours, but real time that took five minutes, then you just need five minutes of spotlight time for the other group, even if that's five minutes of rousting a hobo and then 5:55 of "we go somewhere and hang out."
If they need ideas for what to do or you want to spring things on them - that's why God created random encounters, right? Either they self-motivate some mission oriented stuff, which you come up with, or they mess around in a tavern or go shopping, which you come up with, or they sit around looking glum till a land shark attacks them, which you come up with. You do anything you'd normally do to the full party, but ideally with slightly less kill. (Or not, if you want to dissuade them from splitting in the future.)
If they are content to wait in the bar, let them wait in the bar. Have fun bar things happen. People hang out in bars in real life, it's fun. And sometimes good and/or bad things happen, hence the larger than usual incidence of hookups and cop interventions in bars. All you need is for them to all be having fun and getting roughly equal "spotlight time" (time they get to actually do something at the game table).
Not everything has to be mission related or be a "subplot." They can just find out interesting things about the world they're in. If every story everyone ever tells them is a "subplot," then you get into a bad rut where their expectation is that anything that happens in the game world is FRAUGHT WITH MEANING, and it can't just be some guy BSing about how he fought a troll armed with a spoon once.
In my campaign, I make sure there's a healthy amount of "the world doesn't revolve around the PCs" stuff going on. Not only does it make for a realistic feel, but then when someone wants something to do, they have the expectation that "Hey, I can just go out there and go shopping, or find a bar, or find something to do - I don't have to be 'working through a plot element'" every damn minute of every damn day.
In my Pathfinder campaign recently, the party split. One half was going to do something on task and important. I don't even remember what it was and they probably don't either. The plan was to meet up at a known bar later that day. The other half of the party decided "we'll just go wait at the bar now." I roll a random encounter - giant cockroaches. They get to the bar, and the owner, "Ball-less Bill," an old ex-pirate with one leg, one hand, one eye, and apparently less then one thing down below, was standing outside the bar holding the door shut. "What's the problem?" "My basement flooded and there's these big ol' cockroaches running around in there! They're as big as dogs!" "We can take care of this! Stand aside, Bill!" The two PCs bust in and the cleric casts Call Lightning. The cockroaches are like CR 1/4, so they run all around and out into the street as the cleric blasts lightning holes in everything in sight. The fear of God is put into the local yokels, and the cleric gets an Infamy Point (the equivalent of a Hero Point in my pirate-oriented campaign). They yell "Wooo!" and go in and drink for free.
The other half of the party... They did something on mission. Got some information or something. Who cares. No one remembers that, but they remember the Great Roach Holocaust.
If you have proactive players, this shouldn't be a problem. If you have reactive players, then don't treat them like proactive players and give them 'things to follow up on.' Have the world turn, and its events happen around or to the players. If they decide to just go find another bar rather than chase out the giant cockroaches, fine, then make them choose whether they're drinking "bloodwine or dwarven grog" and go back to team A. Seems to me like you're overthinking this by requiring all events to be part of some big Mythic Plotweb.
You have an active engaged player. Run with it!
I can tell you from experience that if you railroad them back onto the tracks, they are unlikely to ever be as engaged about your campaign again.
If you want to tell a story without outside input, write fiction. Dungeons & Dragons is a Role Playing game, the player should be allowed to agency to control their actions and see the world react.
It sounds like you've plotted pretty far ahead and have very specific things that you need to have happen in order to tell your story. Relying on a PC to kill a specific NPC is very risky. Players will develop morals at the oddest times throwing your plans into disarray!
Step back and do your planning from a wider scope. Instead of triggering off of the NPCs death, put a clock on the discovery of the secret mine. If it hasn't happened by September 3rd, then something bad happens. If it's discovered and the intrusion is noted, then the PC is confronted by the NPC (Your original line). If the PC accesses the mine and it isn't discovered that should be a very good outcome giving the PC a jump on the next action. (Try to avoid mandating that the PC is discovered, if precautions are taken, they should be rewarded if the dice are favorable).
By doing your plotting a level up like this you can ensure that your campaign moves ahead while giving the PC free reign to go about it as he or she wishes.
Best Answer
You're not doing anything wrong. Having players guess a plot development doesn't mean they know (unless you're confirming their guesses — don't do that, that is doing it “wrong”). It just means they have put together the puzzle and think they know how it's going to work out.
This is fine! They don't know they're right until they get there. And when they do, as a player it's a great feeling to finally witness the plot unfold and think “I knew it!” It's actually its own reward, in many ways, so you don't want to take that away from them.
Let your players have their feeling of well-earned smarts. They will be on the edge of their seats until the reveal, wondering the whole way whether they will be proven right. This is way better than the opposite — and much more common — problem where you have players who never catch any hints or forget important clues.
Also, as a GM you have all the information, and it's easy to underestimate how easy it is to guess the big picture. This is deceptive though, and can lead you to overestimate how confident your players are in their deductions, and to underestimate how much mystery is left in their experience. In reality, as a player it's actually pretty hard to be sure you're right about your guesses. Even when I've been a player and turned out to have guessed 100% right, I have never been sure until the reveal. The GM's omniscient perspective is often misleading.