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The time-asymptotic pulse shape of absolute and convective instabilities is determined analytically, expanding pinch-point analysis of the Green function (Briggs, 1964) to the case of relativistic-electromagnetic instabilities in three dimensions. The differential equations for the pinch points in the observer's frame of reference are obtained; the case of a relativistic electron stream with effective average momenta acting both along and across a constant magnetic field is examined as an example; and the implications of the results for the investigation of relativistic stream interactions (as in free-electron lasers and cyclotron masers) and hot-electron-plasma instabilities (as in intensely heated mirror-confined laboratory plasmas and some astrophysical plasmas) are discussed.