If you pause for too long after announcing your tutor, you may get busted by a judge for trying to deceptively gain information about your opponent's hand.
IMO if you're not saying it in the same breath, you're not playing it properly. There should be zero pause. If you are going to sac the LED, your opponent should not have a chance to even say "OK" to the spell you're responding to. If you say "Burning Wish sac LED in response" there's no room for error or misinterpretation. You shouldn't be announcing spells, then contemplating whether or not you want to add further effects. It's an all in move, and a single move at that. If you break "Burning Wish" and "in response sacrifice Lion's Eye Diamond" with a pause, you're inviting all sorts of problems and potentially cheating.
Mostly correct, although i would hesitate to say you're potentially cheating if your intent is not to be duplicitous and gain extra information. However, I would agree with what ELD says here. If you give your opponent the impression that you're passing priority (as you usually do), you are probably playing the spell wrong. In other words you need to make it immediately clear that you are maintaining priority. I would be very suspicious of a player that announced Burning Wish and tried to get a read before deciding whether to crack LED or not.