According to Wendy, a rotating 4D planet, regardless of whether it started off with two different rates of rotation or not, would eventually settle into a Clifford rotation (two equal rates of rotation), because that is the state where there is no tidal tension between the two rates of rotation.

A Clifford rotation is peculiar in that it is, to borrow a term from chemistry, racemic: the spiralling motion of any given point on the planet becomes symmetric with the motion of any other point via a symmetry operation, so that you can no longer tell where the two "rotational poles" are.

Every circle traced out by a fixed point on the planet is a great circle and they all rotate at the same rate, so you cannot tell them apart anymore, unlike the case when there are two distinct rates of rotation, where you can identify two specific great circles orthogonal to each other at which the different rates of rotation are happening. Under a Clifford rotation,

every point on the planet traces out a great circle that can equally be considered as the "equator" of the rotation as any other point. The planet thus "loses" its orientation, in the sense that you can no longer uniquely identify the two planes in which it is rotating, but

any two orthogonal planes would serve that role equally well. However, the rotation still retains its chirality, so in some bizarre sense you can still distinguish between planets that rotate "forwards" vs. "retrograde", even though they no longer have a unique orientation.

When you have two different rates of rotation, the path of any fixed point on the planet would be spiral rather than circular; thus one might argue that it represents a higher energy level. The planet would also have a clear orientation where one plane rotates faster than the orthogonal plane. Because of the anisotropy of the spiralling paths, it seems logical to expect that over time some of the energy of the faster rotation would transmit to the slower rotation, until the two equalize and the planet settles into a Clifford rotation.

Eventually, once you have a Clifford rotation, you no longer need two different periods in your clock.

But I'd expect that you might need a compass with special features in order to help you find your way across a landscape that has no fixed frame of reference like North/South poles.