Thanks for the suggestions. It will be a little while before I get back to messing at this but in brief
1) It only requires the finder to be on and a radio nearby to hear it.
2) Since I pick it up on my hand held (which is not connected to the boat's electrical system), I believe that's good evidence that it's radiated.
3) I did move the antenna cable away from the sounder and that didn't solve the problem.
4) The sound is like Joe describes. It's clearly coming from the pulse to the transducer - It change frequency as the depth range changed (for shorter depths the bleeps are closer together than at deeper range settings).
Since moving the antenna cable didn't solve the problem, the idea that the antenna was the transmitter for a radiative pickup is out the window. So now I need to work on hunting down other possibilities. My first thought is to try to temporarily power the sounder from a separate 12V battery on the theory that the sounder current draw through long power leads is the source of the radiations. If that doesn't solve things, I might try moving the transducer lead. For now I've other problems to fix. The truck wouldn't start this weekend after filling with gas on my way to Neah Bay - the lights were left on for about 10 mins - I think I need a new battery. Also, the sleeve on the idle cable on the port side engine parted near the connection to the engine so I have to figure out how to fix that.
ON THE BRIGHT SIDE - fishing at Neah Bay was GREAT! We limited on salmon yesterday and caught 3 on the half day we fished on Fri. Also caught some cod. First day, I fished with me and a friend and on Sat his son was with. Yesterday was three large kings - 2 in the teens and one about 25#, plus 3 silvers over 6#, a nice 8# cabezon, several china cod a few kelp greenling. My friend and his son just returned from a trip to Alaska and have a full freezer so I was luck benificiary of most of their fish. I'll post a pic of the large king in my photo album shortly.