Out of the question, it has no definition which is only related to physics. Well, there's the "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" definition, but this was chosen to match the celestial-based unit related to the Earth's rotation (which does not tell anything to extraterrestrials).
Wouldn’t be required. Take any frequency, Hydrogen in this case, and multiply it by pi which is unitless. The resulting frequency is pi times whatever you started with no matter how you count the passage of time.
The question the choice is answering is where do you put a signal where other intelligent minds might look for it, yet which isn't at a frequency where the universe is particularly loud in ways that will make detecting your signal harder.
The signal is always going to be modulated, unless the source is maintaining a position with zero relative velocity to the Earth, or deliberately compensating for same - both of which would be far more impressive as a "hello" than a random-ish number which will always be distorted by orbital and proper motion.
Otherwise it's going to have a varying frequency - maybe not by much, and maybe not quickly, but certainly not static.
"ringworld" had a nicely poetic passage about how the 21cm band had been swept clean by all the hydrogen in the universe and was therefore a natural frequency for aliens to try establishing communication over
