Why does this fluorescent ceiling light go out after a few seconds (every time)?

I have a strange problem with a fluorescent ceiling room light. There are four small fluorescent tubes. One day for no apparent reason they all just suddenly went out.

When I turned the light switch off and then back on, they turn on for a few seconds then went out again. I can repeat this any time.

Note that the two tubes on the left turn on instantly but the two on the right show a short (half-second?) delay at which time the orange glow of the filament inside the tube is visible.

How might I go about debugging this and eventually fixing it?

note: I live in Taiwan (120 V, 60 Hz), most electrical fixtures and appliances here are pretty standard. My apartment building isn't very old but watching the flickering of the light inside the switch I'm pretty sure that it's the old neon lamp type rather than an LED.