Have done a few scenes like this before. Not sure what you mean by broken though, is that a state other than flickering? Most scenes like this seem to be variations of flickering.
It's definitely worth recording some as the 'plink' sound you get from them all is different, as is the buzz and and hum. For the long tubes you can use some worn out starters to get different states from them. For spot effects, close miking different areas of the light is the way to go. I also remember getting some interesting contact mic sounds from the tubes. It would be useful if you can get access to some areas with lots of lights hanging, as the cumulative effect is different and useful for background atmos. Old offices are good for this. Getting your recordings to sync with what's in your film is all going to be done in the editing though, so leave plenty of time for cutting these together. You can make loops with nice hum sections to make this a bit easier.
It's worth also noting that quite a lot of sounds for this sort of thing are designed from other elements, so you don't necessarily need to just use the actual sounds. You can get away with all sorts of electrical buzz and crackle, so record anything in that category.