I want a different sound to play when the Second Chance is activated. I tried pointing the sound event in sounds.json to another sound file, but to no avail. The sound I want is minecraft:entity.blaze.ambient, or more specifically, minecraft:mob/blaze/breathe3.ogg. Help...?

That worked! Thank you, I'm new to making datapacks for modded things, so please forgive my ignorance. I appreciate the help.

Of course! Do note that your changes might not apply if your resource pack is below the default vanilla pack in the list.

You need to make a sounds.json file in assets/secondchanceforge/sounds.json and replace the player.classic_hurt sound definition. Remember to use "replace": true. Have you tried this yet?