The FAA variously describes night starting at: sunset, civil twilight, an hour after sunset.
Right now here those times are 5:11PM, 5:39PM, and 6:11PM.
Amusingly (while not used by the FAA) there is also astronomical twilight (6:42) and nautical twilight (6:11).
Slight quibble, I believe there's only one definition of "night", and it's civil twilight (61.1). The other uses of "when it's dark outside", for navigation lights and for currency, don't redefine night, they just tell when the nav lights must be on or you have to be current.
The reason for the "N/A" is not just administrative, there is a real risk to life safety.
More quibbling, since I guess I'm in the mood. Sometimes it is effectively administrative.
There are primarily two reasons for a procedure to be NA at night:
1) Unlit penetrations of the 20:1 visual surface that extends out from the end of the runway. Most typically, trees. During the day you can see them, at night you can't. They are tall enough to pose a danger, so the procedure is labeled NA at night.
2) No official obstacle survey for that runway end. This means there may be obstacles, or there may not be, but since it can't be determined to be clear, the procedure is assumed to have unlit penetrations and the procedure is marked NA.
With #2, there are many, many cases where the 20:1 visual surface probably IS clear, and night operations could be performed safely just fine, but with no survey there is no way to prove it. So, in essence, it's an administrative reason.
Of course, as the pilot you don't know if it's #1 or #2, so the smart pilot will assume it's #1 and not press his or her luck.