  We show that in electron-hole bilayers with excitonic order arising from
conduction and valence bands formed by atomic orbitals that transform
differently under inversion, nonzero interlayer tunneling leads to a second
order Josephson effect. This means the interlayer electrical current is related
to the phase of the excitonic order parameter as $J = J_c \sin2\theta$ instead
of $J = J_c \sin \theta$, and that the system has two degenerate ground states
that can be switched by an interlayer voltage. In a three dimensional stack of
alternating electron-hole planes or a two dimensional stack of chains, the
second order Josephson coupling can lead to a Weyl semimetal or a quantum
anomalous hall insulator, respectively. A generic order parameter steering
effect is demonstrated, whereby electric field pulses perpendicular to the
layers and chains can steer the order parameter phase between the two
degenerate ground states. The steering is also applicable to the excitonic
insulator candidate Ta$_2$NiSe$_5$.
