I can remember two tail pipe fires in my time.
In BAH we used to do compressor washes on the B732 JT8 engines using a mix of demineralised water and 5% JetA1. One day, unknown to me the rig had been filled with nearly neat kerosene! On the post wash run the fuel in the jetpipe caught fire during the start, ran out and then ran back under the engine. Being quick thinking (in my youth) I let the engine run up to idle until the jet pipe fire went out, then shut the engine down and extinguished the flames under it with a fire extinguisher which we had with us.
The other one was a CX B742 on the ramp. For some reason the CX engineer wanted to test the ignitors during the transit. What you do is to trip the HPSOV CB, then open the fuel/ignition switch. He tripped the ignitor s CB instead. When he had walked down to the engine to listen to the ignitors, the fuel had ignited itself in the hot engine. We changed the engine for him.