The guy whose backyard adjoins ours.
His porch light dims, brightens, turns on and off.
Perhaps he is signaling aliens, commies or terrorists.
Is it on a motion sensor and it’s seeing bunnies & such running around in the yard? Our across-the-fence neighbors in St. Paul had a motion-sensor light that would turn on whenever we walked into our kitchen in the middle of the night.
Motion sensor.
When my cat gets out at night (which is not supposed to happen but he’s sneaky) I can track him through the neighborhood. And back.
If there’s an energy-saving bulb in the motion sensor then it comes on dimly at first, and if it goes out quickly, it never gets all that bright. Only after it’s been on awhile.
I don’t believe it is a motion sensor, it is always on.
You said it went off. Maybe it’s just a short in the wire.
Paranormal activity is said to affect the performance of small electronics such as lights, so perhaps your neighbor’s house is haunted.
Or, the bulb’s giving out.
That was my second thought, the first being branches blowing in front of it, but the light still burns and the house hasn’t caught fire after my observing it all Winter.
I have a few spotlights strategically mounted around my house that have both light and motion sensors. During the day, they are off. At night, they are always on, but dim. If they detect motion, they brighten for about 3 minutes, then return to dim. The motion sensors are pretty sensitive, so it’s taken some fiddling over time to get them set so that they aren’t constantly being set off by branches and distant motion. I suspect your neighbor has these types of lights and hasn’t bothered adjusting the motion sensors to limit their activation.
cataracts maybe.
Perhaps so. 
Lots of theories already mentioned. Let me add that there could be a small black hole orbiting in your neighbour’s backyard. It absorbs the light you see when its orbital path passes between the porch light and you.
I prefer that theory to cataracts.
That was my first thought as well. You can usually tell if it’s a high pressure sodium lamp because it’s one of those ones you see with that orange tint to the light. Mercury vapor lights are more of a white-blue light.
I felt like my MIL, but I brought out the binoculars.
It is indeed a motion sensor, as Ethilrist suggested.
“Gladys, will you Please leave the Stevens family alone…!?”
Had to be said…
I was driving home on night when I saw a porch light doing exactly that, rapidly. It was on an old, rock house that sat alone by the highway. Due to some high school pranks, I knew an older man lived there, but I had never met him. See, if anyone stopped a car in the road in front of his house for more than a few seconds, he would come out yellling and screaming for you to leave. Then we would take off at high speed, immensely enjoying our wittiness. Some fun, huh? Since this was a good 10 years after I graduated high school, I started thinking that the gut must really be old now and maybe he was having a heart attack or stroke and could only reach the light switch. Maybe he was deperately signalling for help! Probably partially due to the grief I had helped cause him in HS, I turned around and went to investigate. I got out of my car and knocked on the door. After a moment, he opened the door and the following conversation ensued:
Old man: Is he out there?
Me, looking around: Is who out there?
Old man: HIM! THAT’S WHO! Spends all his time sneaking around my house and hiding in my bushes
Me, looking around again: I don’t see anyone…
Old man, wild eyed: OF COURSE YOU DON’T SEE HIM! He was in Vietnam, you fool! You won’t see him unless he WANTS you to see him!
Me, getting a clue: Yes, well, that does make it difficult, then. I’ll look around more on my way out. Have a nice evening!
I got into my car and drove directly to the police station. I explained the situation to the desk clerk. When I was finished she said “Yes, Mr. Whosit. He’s one of our favorites. We’ll send an officer by to calm him down”.
So you might want to go check it out. Could be worth a story!
I only WISH my neighbors had their lights on a motion sensor. They have these exterior lights all around their house, shining up at the house, down at the bushes, over the porch etc. They leave them all on ALL NIGHT LONG, every night. Maybe a dozen 150 watt bulbs.
We’ve asked them about it, and the excuse was that the children were afraid of the dark. Hmmmm… This would explain leaving them on while they went to sleep, but at 4:00 am? My working theory is that one or both adults are paranoid about security, or are themselves afraid of the dark.
It could have a “dusk to dawn” type light sensor that is just a little too sensitive, so the brightness of the bulb itself causes it to dim and/or turn off. Rinse and repeat.