Does the eternal signal have to be a non-causal signal?

Not necessarily, but the non-causal signal must be a signal without time.

The signal system should have an input signal and an output signal. If the output signal is only related to the present or past time of the input signal, the system is called a causal system, and the output input signal is a causal signal; otherwise, it is a non-causal system and a non-causal signal.

Causality system means that a system is "causal", that is, the system satisfies causality. Causality system refers to a system in which output (response) occurs only when the input signal excites the system.

Time domain judgment: the impulse response function h(t) of the system, when t0, h(t)=0, indicates that the system is anti-causal.