I don't have much experience with play-by-email games, so these are probably less useful in that context, I'm afraid.
Don't be subtle.
For any of these strategies, tell the players straight up what you're doing and why. Solicit their opinions and ideas, and create space for feedback about the techniques once they're being used. This creates an atmosphere of trust and mutual accompaniment toward mutual goals, instead of a sense of manipulation and mistrust. The best social engineering is the kind where you enlist the targets as willing participants.
Start earlier.
Provide a time and space for the group to socialize, catch up on what happened that week, and get the giggles out before you try to do anything game-related. How much time this requires will depend on your group.
Provide transition cues.
Playing music during the pre-game socialization and then turning it off, or starting up game-specific music when it's time to settle down, can be very effective. Other techniques include having everyone wash their hands (no, really, it works!), moving from one room to another, saying a prayer, ringing a bell... you get the idea. Be creative and find something that suits the reality of your group.
Don't forget to transition out of the game at the end, too!
If necessary, impose gentle carrot-and-stick.
The nature of the reward and punishment will depend on the group, and this requires group buy-in or it'll seem arbitrary and mean-spirited. But if you can get it right, rewarding the group for staying on-task and gently reprimanding those who don't can be effective. But don't lay this down from on high as the GM; this needs to be implemented by the collective or they'll balk.
Remember that rewards and reprimands can be very simple: often simply having behavior called attention to provides the requisite pride or shame. Combine with the transition suggested above: it makes for clear demarcation regarding when the carrot/stick dynamic is or is not in effect.
I do several things to keep the player characters interested and invested in each other.
- At the start of the game, I insist that players coordinate backgrounds (subject to my approval) such that each character know at least one, and preferably two or more, of the other characters. In general, I prefer these connections be positive; the most negative I will usually tolerate is on the order of a friendly rivalry. In general, I also prefer that if you start from any one character, you can get to any other character by following these pre-arranged links. (In graph theory language, the players are all connected, although indirect connections are fine; the alternative would be two more more sub-groups connected internally but not to each other.) And finally, I try to ensure that each connection is more than trivial, but not necessarily life-binding.
So for instance, "We met in a bar twenty years ago and never saw each other again," is trivial. "We are cousins who are best friends and we are rarely separated," is life-binding and more than I look for (although it's fine if that's what they want.) Things like the following are what I look for, and/or what I've seen in the past:
- Our characters served in the same unit years ago, and knew each other, but haven't kept in contact...
- I served as a mercenary escort once, while he was travelling with his master from here to there; along the way, this happened....
- We weathered the siege/plague/earthquake of wherever together some time back....
Now, some players are genuinely not wired that way-- if you ask them for backstory, they freeze; if you given the one, they can't connect to it. When I run into a player like that, I have to respect that, but I try very hard to get everyone to adhere to the guidelines.
That does not directly solve the problem. (It actually solves the problem of getting the characters all on the same page at the start of the game.) But it does often give me enough to work with to do the following:
- With enough insight into character backgrounds, and with overlapping backgrounds, I try to give every character an mid-term to long-term goal or plot arc, and then I try to modulate that by giving at least one other character a minor to moderate interest in how the first character's arc plays out.
It's important (to me, for the games I want to run) that these arcs not be strictly opposing: If one character has sworn blood-vengeance on an NPC, I won't give another character the goal of keeping that NPC alive. But I might give another character the goal of getting something from that NPC before his death, or getting the NPC to do something, etc.
And I also try to modulate this in another direction by giving other characters-- ideally, not the same one-- influence over the plot lines. So continuing that thought:
- Player A has sworn to kill Sir Odious, his parents' killer
- Sir Odious has information that will help Player B in her quest to do something else
- Player C knows someone who can be bribed into giving up information about where Sir Odious will be
In that way, for each of the various player sub-quests going on, at least one or two others will be involved somehow, even if only at the periphery. Ideally, Player B has some motivation for something to happen, and Player C has something he needs-- something at least moderately costly or risky. They are invested.
One thing I would not do-- at least not again-- is what you tried:
I've had players create characters (with backgrounds) completely secretly from each other with the hopes of allowing the character interaction to be heavily role-played at the table. Didn't work because of very incompatible characters.
I've never done that, specifically, but I've inadvertently done similar things and it never worked well. It seems like it should work, especially if you pattern it similar to what I've outlined above, but there's a structural weakness to it: If the players, starting out with the relative blindness of only knowing their little part of the background, they just might not see those connections you built in for them, and won't give themselves the incentive to start sharing information. And if your players were the sort that would do that naturally, you wouldn't have to go through these acrobatics in the first place.
Best Answer
The first thing to do is talk to the players. They should both be made to agree that minor compromises for the sake of everyone having fun. If everyone fights everything that you do, it won't be as fun.
Serious vs light guards is common
One book series I find very inspirational when talking about guards is Colon and Nobbs from Terry Pratchett.
They steal from their office, they aren't good fighters, they make rude and silly jokes, they take food bribes from lots of people for their service. They are high on the silly end of silly.
But, they also have their ears to the ground. People appreciate their silly nature and don't find them scary as guards. They tell them everything. Several times they save the day with their unassuming natures.
Likewise, Hot Fuzz is a famous and similar example.
Work with your light player to find a backstory for them that works to help immersion. A lot of guards are incompetent and have bad attitudes, but still manage to get the job done when it counts. Work out why the silly one is more valuable than other guards. That way, they'll look a bit more serious without them compromising their personality.
Have reasonable timelimits on ooc actions, and reward bold and decisive action
People spending forever planning is a serious character flaw. If the serious player is doing that, then have it be a thing in story. If they can't make a decision in a reasonable period of time, then ask the lighter player what they are doing, and roll with their plan. Let the serious player spend ages planning, while the other players get stuff done.
Make sure your world isn't so unforgiving that a quickly made up plan will fail, and roll with it. The casual attitude of the lighter player can help solve the problems, and make them useful.
This will encourage them to delay less, as the other players are getting fun scenes while they think.
Talk to the player about spotlight time
As you said, they like thinking a lot and spending a long time planning. Which is fine. But do remind them, there are other players who like to do things, and spending the entire session focusing on solely their concerns isn't fun for the other players. So talk to them.
Say something like "I know you are having fun, but what you are doing is making it less fun for the rest of us. Could you this session hang back more so that others can get a chance to play their characters. It's not that we don't like your character, but we want a chance to play our characters and NPCs as well." And if they chose to keep spending entire sessions focusing the spotlight on their character, you know they're not willing to compromise.
If they want to spend five minutes plotting, that's fine, but that's five minutes of their time in the spotlight. Other players should get a chance to play out their characters after and you should get to use your NPCs, who don't care about planning as much.