  To each automorphism of a spherical building there is naturally associated an
"opposition diagram", which encodes the types of the simplices of the building
that are mapped onto opposite simplices. If no chamber (that is, no maximal
simplex) of the building is mapped onto an opposite chamber then the
automorphism is called "domestic". In this paper we give the complete
classification of domestic automorphisms of split spherical buildings of types
$\mathsf{E}_6$, $\mathsf{F}_4$, and $\mathsf{G}_2$. Moreover, for all split
spherical buildings of exceptional type we classify (i) the domestic
homologies, (ii) the opposition diagrams arising from elements of the standard
unipotent subgroup of the Chevalley group, and (iii) the automorphisms with
opposition diagrams with at most $2$ distinguished orbits encircled. Our
results provide unexpected characterisations of long root elations and products
of perpendicular long root elations in long root geometries, and analogues of
the density theorem for connected linear algebraic groups in the setting of
Chevalley groups over arbitrary fields.
