  We propose a holographic formalism for a timelike entanglement entropy in
non-conformal theories. This pseudoentropy is a complex-valued measure of
information, which, in holographic non-conformal theories, receives
contributions from a set of spacelike surfaces and a finite timelike bulk
surface with mirror symmetry. We suggest a method of merging the surfaces so
that the boundary length of the subregion is exclusively specified by
holography. We show that in confining theories, the surfaces can be merged in
the bulk at the infrared tip of the geometry and are homologous to the boundary
region. The timelike entanglement entropy receives its imaginary and real
contributions from the timelike and the spacelike surfaces, respectively.
Additionally, we demonstrate that in confining theories, there exists a
critical length within which a connected non-trivial surface can exist, and the
imaginary part of the timelike entanglement entropy is non-zero. Therefore, the
timelike entanglement entropy exhibits unique behavior in confining theories,
making it a probe of confinement and phase transitions. Finally, we discuss the
entanglement entropy in Euclidean spacetime in confining theories and the
effect of a simple analytical continuation from a spacelike subsystem to a
timelike one.
