Yes, we did have a similar problem, only the symptoms where much worse. I replaced all three coils, wires, connectors and plugs. That solved that problem.

Is it possible that circuit in the stop light switch is bad which is giving code 5 at pin 14 even if the brake lights are still working?

I'm beginning to think more about pulling the harness and repairing it if needed. I will check the date tag first.