I'm actually not so much interested in sunrise/sunset times. What I want to know is how to relate local planetary coordinates (e.g., planetary lat/lon) to, for example, heliocentric coordinates at a given time.
Mike G. recently asked Where can I find planetary rotational axis direction? which received a useful answer. It's most of the information I want, but there's one degree of freedom remaining.
One also needs the rotational angle (relative to local noon, say) of the planetary prime meridian at a given moment (or equivalent information).
I think, for example, this angle is relatively easy to determine for the planet Mercury. Mercury has its rotational period locked to its orbital period. I think that the prime meridian of Mercury directly faces the Sun at the moment of perihelion. But how do you do this in general?
I'm not sure how clear I'm being. Another way of trying to ask (basically) the same question (this time for Mars) is as follows. Suppose that I know the Martian coordinates (lat/lon?) of the Perseverance probe at a particular time of interest. How do you know where to aim an antenna from Perseverance to Earth at that moment? You know where both the Earth and Mars are: that's not the problem. The problem is knowing the direction Mars "faces" at that time.
Is the information I want available for the planets? How is it specified?