The perception of time (as duration, reference to events, and reference to internal clocks) is a feature of cognitive processing, and not an alternative to physics.
What if it is not a mind construct, but actual perception of physical time as it is described by physics and maths and observed as part of space time? That is my hypothesis, that as we perceive chemicals with smell and taste, and electric fields with touch and light with vision, we perceive time with this brain thing, and the more accurate the perception, the better we are at constructing causality and predictions.
What I am thinking is that the concepts we use to describe time are secondary to the actual perception. Concepts are constructs of our awareness who tries to create knowledge to improve prediction accuracy.
That means by perceiving time I mean receiving sensory information about the property of spacetime, time, as it objectively exists in reality.