It's symptomatic of a bad solder joint. Just reflow all of them. I can't be more specific without the amp in front of me. It could be a heater connection as Grainger suggests. It could also be a ground connection, tube socket connection, power supply connection, or something else. If you want to flip over the amp, turn it on and poke around at various connections while you listen you can probably find the offending one. But you can get a bit of a zap if you are not careful and if the bad connection is in a place that makes a lot of noise when you work it around you could damage headphones. So you would have to decide if you want to take the responsibility of testing that way - or just check everything you can with a magnifier and reflow the solder joints with the amp off and disconnected from power and headphones, then hook it back up and see if the probem is solved.
Another way to look at it is this - PB would redo every joint if it came in for repair, because it would cost me a lot less of his time to do that than having him fart around trying to figure out which individual joint to reflow. And if we sent it back with the offending joint fixed and then a different one went loose because, say, all of the solder joints were a little shaky due to builder inexperience, we would look like poltroons. So we just do them all in ten or 20 minutes, check it out, and send it home confident that all the solder joints are now solid.
So I still say do them all, and if the noise is still there we will move to plan B.
