To be honest, I can't recall ever playing a game with timed events such as this. Yes, there are plenty with timed events, like the Death Snares in Bard's Tale 2. But you DIE if you run out of time there, or in other games simply fail.
I had a similar idea, but abandoned it simply because of (amusingly) time constraints. It takes a lot more to develop properly. But then, I'm solo, and you have a team. I just hope Corwin doesn't develop and write like he plays DDO. (Where are you at? I went down the wrong way. AH! a spider is killing me, oh I'm dead. Someone get my soulstone.)
j/king
For the stolen diamond example, you have several options you have to consider:
Showing up before the theft, but leaving. This gives the thief someone to frame.
Showing up before the theft, and stealing it. You still get blamed, fairly though.
Showing up before the theft, and staying until the thief gets there. From here, you can either stop the thief, or steal the diamond and set him up to take the fall.
Showing up shortly afterward, and using clues left to track the thief down. This can branch into you returning the diamond, or hocking it. It can also branch by killing vs turning in the thief.
Finally showing up long afterward, when all the clues have been trampled by inpept inspectors, and you have to go on less information. Which either leads to failure to find the thief, or the above two options.
5 main options, three of which have 2 or more branches (and two which can lead to multiple branches in the main branches). Then you have to consider the end effects (party reputation, quests given later or not given later, being chased by dogs and grues, etc).
I wish you well on it, since I want to see how it'll turn out. And DTE nailed it perfectly. Just look at the firestorm Sonic 4 is getting. First return to decent platforming and the series roots, and they're mad because his eyes are GREEN. And the rings are too big. And the BBEG is named Eggman instead of Robotnik.
So make your game how you want to make it. Do your best, and fully expect to be criticized over incredibly stupid things.