  We set up a tree-level six point scattering process in which two strings are
separated longitudinally such that they could only interact directly via a
non-local spreading effect such as that predicted by light cone gauge
calculations and the Gross-Mende saddle point. One string, the `detector', is
produced at a finite time with energy $E$ by an auxiliary $2\to 2$ sub-process,
with kinematics such that it has sufficient resolution to detect the
longitudinal spreading of an additional incoming string, the `source'. We test
this hypothesis in a gauge-invariant S-matrix calculation convolved with an
appropriate wavepacket peaked at a separation $X$ between the central
trajectories of the source and produced detector. The amplitude exhibits
support for scattering at the predicted longitudinal separation $X\sim\alpha'
E$, in sharp contrast to the analogous quantum field theory amplitude (whose
support manifestly traces out a tail of the position-space wavefunction). The
effect arises in a regime in which the string amplitude is not obtained as a
convergent sum of such QFT amplitudes, and has larger amplitude than similar
QFT models (with the same auxiliary four point amplitude). In a linear dilaton
background, the amplitude depends on the string coupling as expected if the
scattering is not simply occuring on the wavepacket tail in string theory. This
manifests the scale of longitudinal spreading in a gauge-invariant S-matrix
amplitude, in a calculable process with significant amplitude. It simulates a
key feature of the dynamics of time-translated horizon infallers.
