  Context. Non-dusty late-type giants without a corona and large-scale
pulsations represent objects that do not fulfil the conditions under which
standard mass-loss mechanisms can be applied efficiently. The driving mechanism
of their winds is still unknown.
  Aims. The main goal of this work is to match the radial velocities of
absorbing matter with a depth in the red giant (RG) atmosphere in the S-type
symbiotic star EG And.
  Methods. We measured fluxes and radial velocities of ten FeI absorption lines
from spectroscopic observations with a resolution of ~30 000. At selected
orbital phases, we modelled their broadened profiles, including all significant
broadening mechanisms.
  Results. The selected FeI absorption lines at 5151 - 6469A, originate at a
radial distance ~1.03 RG radii from its centre. The corresponding radial
velocity is typically ~1 km/s , which represents a few percent of the terminal
velocity of the RG wind. The high scatter of the radial velocities of several
km/s in the narrow layer of the stellar atmosphere points to the complex nature
of the near-surface wind mass flow. The average rotational velocity of 11 km/s
implies that the rotation of the donor star can contribute to observed focusing
the wind towards the orbital plane. The orbital variability of the absorbed
flux indicates the highest column densities of the wind in the area between the
binary components, even though the absorbing neutral material is geometrically
more extended from the opposite side of the giant. This wind density asymmetry
in the orbital plane region can be ascribed to gravitational focusing by the
white dwarf companion.
  Conclusions. Our results suggest that both gravitational and rotational
focusing contribute to the observed enhancement of the RG wind towards the
orbital plane, which makes mass transfer by the stellar wind highly efficient.
