Like you saidIf the rule books for 5e just dropped out of the sky there are a few sources that would point players and DMs to using initiative should be used in situations where you want to track actions closelythings other than combat. The first of these is on pg 5 of the PHB:
Unlike a game of make-believe, D&D gives structure to the stories, a way of determining the consequences of the adventurers' action. Players roll dice to resolve whether their attacks hit or miss or whether their adventurers can scale a cliff, roil away from the strike of a magical lightning bolt, or pull off some other dangerous task. Anything is possible, but the dice make some outcomes more probable than others.
Dungeon Master (DM): OK, one at a time. Phillip, you're looking at the gargoyles?
Phillip: Yeah. Is there any hint they might be creatures and not decorations?
DM: Make an Intelligence check.
Phillip: Does my Investigation skill apply?
DM: Sure!
Phillip (rolling a d20): Ugh. Seven.
DM: They look like decorations to you. And Amy, Riva is checking out the drawbridge?
The DMG hasnext is on pg 7 of the PHB:
- The DM narrates the results of the adventurers' actions.
...
In certain situations, particularly combat, the action is more structured and the players (and DM) do take turns choosing and resolving actions. But most of the time, play is fluid and flexible, adapting to the circumstances of the adventure.
Combining this with a coupleportion of examplesthe note about Combat in the PHB on pg 8:
...
Combat is the most structured element of a D&D session, with creatures taking turns to make sure that everyone gets a chance to act.
along with the text describing initiative on pg 177 of the PHB:
INITIATIVE
At the beginning of every combat, you roll initiative by making a Dexterity check. Initiative determines the order of creatures' turns in combat, as described in chapter 9.
and the text you referenced on pg 181 of the PHB:
In situations where keeping track of the passage of time is important, the DM determines the time a task requires. The DM might use a different time scale depending on the context of the situation at hand.
...
In combat and other fast-paced situations, the game relies on rounds, a 6-second span of time described in chapter 9.
Gives us a good idea that non-combat fast-paced situations should use the rounds system defined in the combat chapter (PHB pg 189):
...
The game organizes the chaos of combat into a cycle of rounds and turns. A
round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative. Once everyone has taken a turn, the fight continues to the next round if neither side has defeated the other.
...
Initiative determines the order of turns during combat. When combat starts, every participant makes a Dexterity check to determine their place in the initiative order. The DM makes one roll for an entire group of identical creatures, so each member of the group acts at the same time.
The DM ranks the combatants in order from the one with the highest Dexterity check total to the one with the lowest. This is the order (called the initiative order) in which they act during each round. The initiative order remains the same from round to round.
The DMG then gives two concrete example of using initiative in non-combat situations Chases (DMG pg 252):
DMG PG 252and Complex Traps (DMG pg 121)
It also has a good example of an effect that suggests close tracking of time is appropriate, Planar Portals on pg 45 of the DMG PG 121:
Time. The portal functions only at particular times: during a full moon on the Material Plane, or every ten days, or when the stars are in a particular position. Once it opens, such a portal remains open for a limited time, such as for three days following the full moon, or for an hour, or for ld4 + 1 rounds.
Some other examples mightBringing all of that information together we would be: able to know that we can come up with inventive ways to use the initiative and rounds system to track non-combat situations.
- If the players are completing a task with a particularly short time limit (eg you have to avoid the guard partrols and there is only a 1 minute gap in the guard that you need to take advantage of)
- You are performing some task that is delicate, and if it goes wrong you need to get out of dodge fast (eg trying to disarm a complex trap)
The DMG also gives the option of Side Initiative on pg 270, which might fit what you are looking for, of close tracking of time, while also giving the players order flexibility.
DMG PG 270
I've put together an example of applying this initiative variant to a non-combat situation. Drawing on your option of a non-dangerous round-based effect, the DMG provides something which fits the bill, I think Planar Portals with a time based requirement (DMG pg 45detailed above): fits the bill.
Time. The portal functions only at particular times: during a full moon on the Material Plane, or every ten days, or when the stars are in a particular position. Once it opens, such a portal remains open for a limited time, such as for three days following the full moon, or for an hour, or for ld4 + 1 rounds.
