Ceiling Fan Light

Does the fan assembly incorporate the light and if so do they have separate pull chains

If not is the light somehow independently controlled and if so how

You may have a short some place. With the power switch off, take off the housing of the fan to inspect the wiring for both the fan and light. Reconnect both wires securely, then try again.

Or it might be a malfunction of an electronic switch. That's why I asked whether the light might be otherwise controlled

It could be as simple as the light socket in the fan and the bulb aren't making a good connection. Change the light bulb to a new one and see if the problem goes away. I've had this happen in a regular lamp. The heat builds up with the bulb being turned on within a few seconds and the connection becomes an open circuit. Also it's possible the light socket may need replacing.

Something is heating up and open circuit is happening.

I believe if it were short the circuit breaker would trip. Perhaps an open.

You might be right. We just haven't had our circuit breaker trip for several decades now. However, I must also share the fact that many of our wirings are relatively new and/or replaced about five years ago when I had electrical work done to our entire house - built in 1955. I had tv cables placed in every room, new lighting in the family room, and GFI sockets in the kitchen and bathrooms.