From a user's perspective, it will be very helpful to provide an overview of what times are available (think also of the way many cinema/theatre sites show a visual seating plan when booking tickets). As a starting point, you should be looking for something along the lines of the following, where they can both see what times are available, and pick the one ...
Another way is to change the format of the UI when the end date is not defined. Instead of displaying:
March 1, 2019 - N/A
you can have something like:
Starting from March 1, 2019
If you think this may confuse the user, you could easily add an element that clears the confusion when hovered over, like this:
Starting from March 1, 2019 (?)
These timestamps should be very rare; it's just one hour in the 8760 which happen in a year's time. The hour is deliberately chosen in the night, so most people not familiar with UTC (programmers, system administrators, astronomers, military) don't need to register anything in that hour.
That said, one option might be that when a user enters an ambiguous ...
The vacancy period here is quite hard to define unless you have a start and an end.
If there is no end date then it's not a period but a state.
Therefore I suggest splitting the logic here into two parts:
Vacant state (on / off)
Dates for when state is known
So the dates would be : Vacant from: "" Residents will return: " " (unknown return date).
You can look at Omnifocus (a task management app), which has a repeat task option.
They split it into two dropdowns once you select Repeat monthly.
Option 1: select specific days for the month:
Option 2: select days of the week for each month
Update: Another option - make it read like a sentence
You could also make the form to read like a sentence.
I made a mock up just for a reference for the structure since I saw that it was your main concern.
It's important that you show some visual clue in the calendar to different days with/without available hours so the user does not click there in vain.
Hope it helps.