Above is my "breadboard".  The coils separated about 4".  Here's the input coil & 100 pF cap.

Here's the output coil & 100 pF cap.  There's little chance for coupling across 4" of space.

Above is my scope probe connected to the output coil.

Above is the probe data.

Here are the nasty twin-peaks trace, when sweeping from 3 to 5 MHz.

Here (above), I've removed the probe and substituted a simple clip-lead & shielded cable.

Above is the display generated when using the clip lead and sweeping from 3 to 5 MHz.

Here is my original sloppy circuit, but this time with the clip lead instead of the scope probe.

And above is the trace generated with the sloppy circuit & clip lead instead of scope probe.