REPRINT: Sign in Blood.

The reminder text is questionable. Night's Whisper would be an usable variation at common, but this felt like a good place to tackle with the idea of targets / targeting.

Here's more on 'targets' just to get some sense of what we're dealing with here.

What do you mean with "if any"? The reminder text is on a card with targets, so you don't talk around that by adding confusing references to how other cards work. Also we already have the phrase "as you cast", so no reason to not use the simple phrase "(Choose the target as you cast this spell.)" (And adapt the reminder text for spells with multiple targets).

The second sentence absolutely does more harm.

Why doesn't this have reminder text that life loss cannot be prevented like damage, but can be replaced by an ability that says so? Also some reminder text about this not being life payment and hence can reduce the life to 0 or less? And that drawing from an empty library loses the game?

Those last two are more relevant reminder text than what you put into the second sentence since they at least have something to do with this card and not "another spell or ability".

Your first sentence already defines the timing of target choice, the second sentence just repeats that information and then goes on to mention irrelevant exceptions.

Actually, with the second sentence I was trying to clear up the situation in which player A says "I cast Sign in Blood targeting you" with player B responding "Okay, but I grant hexproof to myself" and player A going "Nevermind then, I target myself."

And then the opponent points out that the reminder text clearly states that targets are chosen as you cast a spell, not after another player casts a spell.

If you want to put reminder text regarding something as rare as granting a player hexproof anywhere, I suggest onto the card that grants a player hexproof e. g. "You gain hexproof until end of turn. (Spells that only have illegal targets are countered on resolution.)"

Fair enough.