Can somebody explain the steps to troubleshooting a light fixture that has stopped working.

The light fixture on the ceiling of the mudroom of the side entrance to my house has stopped working. During the prior six months, the fixture would work, then not work, then work, then not work. Sometimes a quick on, off, on, off sequence on the switch would activate the light.

After the light stopped working, I tested the fixture's bulb in another fixture and it worked. I also tried to put a new bulb in the broken fixture, but that did not work.

The light is controlled from a switch in the kitchen. The switch actually has two switches. The top switch is for the kitchen (which works) and the bottom is for the mudroom.

I took the face plate off of the switch and the switch is actually made of two separate switches, not a single unit with two switches. The wiring on both switches seem secure. (Both switches are wired together on one side.)

Some additional information, my house was built in 1937 and has mostly knob and tube wiring.

What would be the steps to troubleshooting this light fixture? Aside from replacing existing fixtures, switches and outlets, I'm a novice at electrical work. If this work would require the knowledge of a professional then please let me know.

Thanks,

Andrew