Yes, there is an internal timer for game-triggered interactions (banters). The only way to affect it in script is with two actions:
BanterBlockFlag(I:State*BOOLEAN)
If set to TRUE, it turns off the banter timer. Normally it is set to FALSE. The unmodded game doesn't use this action.
BanterBlockTime(I:Time)
Extends the amount of time before a banter triggers. CUT01G.BCS, part of the cutscene with Irenicus in the Promenade, uses this action to temporarily extend the banter timer for 600 seconds. (I'm pretty sure the banter timer is based on real time, because resting, traveling and pausing seem to have no effect on it. That is, doing those things won't shorten the time until the next banter.) I've only seen this action used once in the unmodded game.
As mentioned, Interact lets you initiate a banter without waiting for the internal timer. I don't think Interact has any effect on the internal timer, but I haven't examined it closely. It could either run independantly of the internal timer, or it could reset the internal timer. The IESDP doesn't say.
By the way, information about timers, script actions and everything else Infinity Engine is covered in the
IESDP.
Also, don't mix your timer variables. If you set a variable with RealSetGlobalTimer, check it with RealGlobalTimerExpired. Likewise for SetGlobalTimer and GlobalTimerExpired. If you mix your timer variables, you can expect unwanted behavior.
The two different time scales are somewhat similar. A value of 600 is 10 minutes if realtime or two hours if game time. The difference comes when you start resting, traveling and pausing the game. Soon the game-time timer value is much larger than the real-time timer value (when you rest, eight hours gets tacked on to the game-time timer, but only a second or two passes on the real-time timer.) When you set a timer, the duration you specify gets added to the current timer value and stored in the specified variable. When the timer matches the stored value, it triggers and a script can act on that. The timer itself, however, keeps advancing.