I think you answered the question a little within your post hix.

Heres how I imagine it.

If a being existed in 1D space-time, the properties of which conform to what we (in 3D) call a binary string. Lets tag those properties (for this thought experiment) from the perspective of the 1D being as black and white - That is, the entire field of perception for the being is either all black or all white.

Given the dimensional constraints, the beings movement is limited to forward/back. Luckily for it though, time still functions.

It would perceive the passage of time via the state changes of the binary string. Black-White-Black-White-Black-White.

The functional constraints for this universe from the POV of the being are;

For all directions of movement.

IF black,

             THEN white.

IF white,

             THEN black.

This is not enough information to understand the underlying spacial structure of the 1D universe.

If the being were to somehow understand even the direction they were moving in - they would instantly be heralded the Einstein of 1D.