What is my toilet up to at night? I’m on the computer upstairs (second floor) between maybe 10 PM and 1 AM. Between midnight and 1:00 I’ve noticed that I will hear a rushing water sound from my bathroom for a short interval. When I’ve been down near there, it sounds like it’s behind the toilet area. It turns off again in short order. No one has used the facilities for a while. What is it doing?
If we go in the toilet, where does the toilet go? And if a toilet flushes and nobody is there to hear it, does it make a sound?
Flapper valve in tank is probably leaking. The level drops where the fill valve opens for a few seconds topping off the tank.
that’s my thought too.
Yeah, I agree with johnpost and Snnipe, too.
But seadoggie01’s answer is a lot more fun. 
Do I need to do anything about it?
Fix it.
(It’s wasting water. And making noises too that might keep you awake at night, if that bothers you.)
It’s a five dollar part and will take you longer to drive to the hardware store than to fix.
Alternative answer, (just because the OP was not explicit about the housing, not because I disagree with the answers given).
Is this in a condo or apartment? Do you share the building with another occupant, either below you or sharing a wall with the bathroom? If so, you could be hearing the sound of another toilet that shares the stack vent. For that matter, depending on the house design, water running through other pipes that are connected to the toilet stack vent can produce a similar sound. (E.g., washing machine or dish washer discharging.) I get that in my house when different utilities are being used. There is a clear, brief sound of water rushing through a pipe, (as opposed to the steady higher-pitched stream of the toilet tank refilling), when water is being drained in sinks that share the drain pipe with the toilet.
I do have a minor nitpick with the answers provided: if the flapper is not sealing, I would expect the tank to be re-filling off and on throughout the day and night, not just limited to one period in the late evening. Of course, that could simply be the time when all the other distracting noises in the house have quieted, leaving that sound more obvious.
In a pinch, I’ve cleaned up a flapper and gotten it working properly, at least for a while.
If the OP is hesitant about fixing this, there are Youtube videos to help out and sites like this one. I recommend Korky brand, not Fluidmaster. When you replace the flapper, wipe off the rim of the drain pipe where the flapper seals to it.
Going by name alone you would think “FluidMaster” would be way better than “Korky”. Heh. I’ve always grabbed one or the other without thinking. Fluidmaster has a nice hanging box display with everything in the box. I’ll try to remember to pick Korky.
I hate the Fluidmaster flappers; they’re flimsy and wear out quickly. Korky makes cheap, durable products.
You would be amazed at how much water this wastes, so do fix it. If you don’t care about the water – for example, if you have a well so your water is free – the extra volume could be overloading your septic field.
Is your toilet running?
Better go catch it!
It does sound like a faulty flapper valve, but…
The OP mentions this happening in the wee hours of the morning. Is it only happening at that time, or is the OP only noticing it at that time? If the flapper valve is leaking, it should be doing this constantly, all day and night, not just during a particular time period.
It’s taking a leak …
Sometimes they fail over time. Our last one would leak every couple of hours, and we didn’t always hear it because of other noise or our absence. It got more frequent and noticeable as time went on.
Most flapper valves begin to leak over time. Most are made of rubber and they get degraded. Be sure to get a replacement valve for your brand of toilet. They are not universal, even those that say “Universal.” BTW, the link states that the chain should be straight, but there should be about 1/4 inch of slack. When the tank refills, it should be at the line on the tank, which is about 1" below the top.
If the toilet is being used periodically in the day, and I assume, flushed after use, there may not be enough water loss between usages to trigger the event.