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Tidal forces slow the rotation down over time, even in space. Also, the sun looses weight as it emits energy.

A black dwarf and dead planet, tidally locked, would still describe an orbit. So long as that functions, any means of being able to signal the positions of the two objects would serve to indicate the orbital period.

Solar emissions are not integrally central to the clock. That source of entropy can be eliminated.

Tidal losses are not integrally central to the clock, that source of entropy can be eliminated.

What are we left with?

Your argument only works in a universe with exactly two newtonian point masses, not a single additional mass. In that universe, time isn't the same as in ours. It is perfectly periodic. That you can't figure out the arrow of time in that universe is actually the smaller anomaly.

Yes: Thought experiments simplify.

That is the point.

My point is, that this is so simplified, that it isn't even a clock anymore.

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