This is from the Pickle Rick episode, where they find Rick's syringe, right?
I've forgotten if it was Morty or Beth who said it; my answer assumes it was Morty. It could've been Beth, but it doesn't really matter for the answer.
"There is a timer set to 10 minutes from now, exactly when we would have left."
I would think that this might be tense-shifted from "will have left" as the clause is about time - although I cannot tell for sure and hence my question. If I am wrong, why is this construction (would+past infinitive) used here?
It's a conditional:
Conditional tenses are used to speculate about what could happen, what might have happened, and what we wish would happen.
Morty is pointing out a syringe (and timer) which had been hidden out of sight. He's talking about what would have happened if he had not spotted the timer.
This fits the Type 3 conditional:
An unreal past condition and its probable result in the past.
- If this thing had happened that thing would have happened.
- If you had studied harder you would have passed the exam.
- If it had rained you would have gotten wet.
- If I had accepted that promotion I would have been working in Milan.
Basically, Morty is implying that
- If we had not found this timer, we would have left 10 minutes from now.
But now that they have found the timer, they have foiled Rick's plan. The timer will not go off as planned, and they might not leave at the same time (if at all).
Morty's statement is a conditional, because his quote implies that the original plan (their departure in 10 minutes) has now changed, because the timer being set to 10 minutes proves that Rick was intentionally avoiding the therapist appointment.
Note that this happens before Beth decides to take the syringe and leave on time anyway. The quote you're referring to, at the time it is spoken, is revealing Rick's secret plan and accusing him of doing something childish. Morty is making an assumption about their plans now having changed (in response to Rick's attempt to wriggle out of having to go with them); and Morty was not yet aware of Beth's later plan to intentionally still leave on time (taking the syringe, as a clever punishment for Rick).
But when you look at your suggestion:
There is a timer set to 10 minutes from now, exactly when we have left.
It should be future tense, since this is addressing a future event:
There is a timer set to 10 minutes from now, exactly when we will have left.
"when we will have left" implies that they will still leave at the planned time, regardless of having found Rick's syringe and timer.
"when we would have left" implies that they were initially planning to leave, but that is no longer the plan (because they found Rick's syringe and timer).
At the time of making the statement, Morty is expecting that their plans have now changed, therefore "would" is the correct choice for Morty here, as it fits with his expectation of the plans having changed.
To make that distinction a bit clearer, let me offer another example.
Imagine if you and a friend are sitting in a plane, waiting to take off. Your third friend, Tom, is still driving to the airport. You get a call from Tom, he explains the situation to you. You hang up, and then say this to your friend:
- Tom is running late to catch the flight. He can only get to the gate 15 minutes after the plane will have left.
The plane will leave at the scheduled time. Tom will arrive too late. This is what will definitely happen.
- Tom is running late to catch the flight. He will only get to the gate 15 minutes after the plane would have left. (Lucky for him, our departure has been delayed.)
Tom will arrive too late for the scheduled departure time. However, due to complications, he will be in time for the actual departure time.
If there had been no delays, Tom would have missed the flight.