EBOW LED help!

i would try an LED and a 470 ohm series resistor wired directly across the output coil and see if it works. it should.. depending on the LED reverse characteristics, it's always good practice to put a reverse bias diode like a 1N4148 across the LED when driving the LED with an AC signal

I think Audioguru is right. If you can't "fluff" the cables or the 2 coils are by necessity close you could try to remove pin 2 from ground and insert a 300 ohm resistor from pin 2 to ground. Then add a 100pf cap from pin 5 (output) to pin 2 (- input). This will give you some negative feedback at the higher frequencies and probably stop the oscillation. The 386 will run a lot cooler as well.