Trying to Understand Spurious Sideband Interference (and some causality problems...)
Think about the Fourier analysis on the single event - this will tell you the frequencies that get produced following the instant that a flat line signal changes to a sinewave shape. That instant in time marks the point at which a whole load of harmonically related sine waves begin and over time (if the initial signal remains a constant fixed amplitude sinewave) all the harmonics will decay to zero leaving just the sinewave.

If you repeat this like someone keying Morse code, the decaying harmonics will not necessarily fall to zero but will, inevitably be reinforced to a peak amplitude at the point when the sinewave is re-activated.

If you think about a square wave and its harmonics the harmonics are there right at the start of the signal activating - this should be no different to any non-pure signal beginning. Note that a pure sinewave never begins - it's been going since t = -infinite