First - get it fixed.
I might be the power company with problems in its lines - if so most likely small tree branches rubbing up against its lines, but it normally would not go on for so long without something getting bad. IF neighbors have this problem, too, it is definately them causing the problem, if not, it may still be them, but much less likely.
It might be something in your house, though. I'd tend to think that more likely and focus on that first since if it is, it could be something you need to take care of soon. Some things that go bad with appliances and wiring can affect all the voltage in the house. I would not worry about your trains right now - I know we get a lot of discussion about installing DSRs and all but frankly I've never had problems with mine and there are more important things to worry about.
More recently, I had something similar to what you describe occur for about three weeks maybe two years ago - when the starting capacitor on my central HVAC unit's main motor went out. Quick dip ever time it started, mild surge (brightening) when it stopped. Simple call to the AC repair guy and around $200 bill for changing it out and doing some other checks and service.
I had a poor connection in my house wiring that was dragging down two circuits upstairs by six volts (definitely enough to see the lights dim alot). I could have hired an electrician but, being somewhat experienced, I spent a Saturday morning tracking it down myself. It was a poor wire-nut connection which I eventually traced to a particularly outlet box and tightened (not get only .7 volt drop). The house is 25 years old now and this sort of thing happens . . .
Wiring problems like that tend to develop oever time and get worse. The concern I always have is not the flicker itself but the probable damage. In the six-volts-gone case above - the six volt dip on a 15 amp circuit meant rup to 75 watts of power disappearing (as heat, somewhere) - - - in this case in that outlet box, where it had melted a wire nut and caused browning of surrounding insulation, etc. A potential fire, (which probably would have been contained in the outlet box which is designed for that) just waiting to happen.
Check with the neighbors first. Hound the utility if you think it is that. Get someone to look at it otherwise. These problems, if in your house, never go away - they only get worse. Maybe not bad-stuff-happens worse, but . . .
