  In this study, we establish a connection between timelike and spacelike
entanglement entropy. Specifically, for a diverse range of states, the timelike
entanglement entropy is uniquely determined by a linear combination of the
spacelike entanglement entropy and its first-order temporal derivative. This
framework reveals that the imaginary component of the timelike entanglement
entropy primarily originates from the non-commutativity between the twist
operator and its first-order temporal derivative. Furthermore, we analyze the
constraints of this relation and highlight the possible extension to
accommodate more complex state configurations.
