Backlight randomly turns off

It can be. We first need to assess what's exactly your machine. To achieve that, you should provide us with the last fourth numbers and letters in your Serial Number, that you can easily find in System Profiler, Hardware tab.

However, short story: yes, it may be the Inverter.

Long story, with explaination: That done, usually a failing backlight derives from four causes, and the latter of those is so unlikely that it almost never happens, unless there are some other causes, like water damage and such alike.

I'll order them in order of parts involved

1. A worn out inverter cable: The cable running from the logic board to the inverter, passes through the display hinges, and in time it wears out and gets pinched in the display. When it happens, the backlight starts to act up, and, usually, jiggling the display up and down restores the backlight for a few seconds, or until the display gets even a small vibration
2. A failing Inverter: Inverters fail, in time. When it happens, they give short burts of energy, with the backlight working for shorter and shorter amounts of time. Sometimes, when it works, it also flickers, pulsating stronger and fainter. When it's overtly damaged, it acts the way you described
3. A failing Backlight: The backlight is given by a small CCFL Cold-Cathode Fluorescente Lamp lodged in the bottom part of the LCD panel. Imagine it, for reference, as a tiny neon lamp. As you know, when a Neon lamp degrades, it starts blinking, taking lots of time to reach heat enough to keep working, shutting down at odd times and, when it works, giving out a degrade hue. For CCFL lamps, the hue is pinkish or yellowish
4. Damaged capacitors on the logic board: As I told, you could chalk it off. Sometimes, the capacitors that push energy in the Inverter cable get damaged. But your machine has less than four years, I'd exclude that.

So, the safest course of action entails changing the inverter, and assess. You may solve everything, or you may need to change the inverter cable too.

I doubt you're going to need a new LCD panel, just the Inverter. If you're unlucky, the inverter cable. That's all.

With your serial number, I could show you the needed parts on iFixit.