How this mod works:

-When you have a parachute it will show on your back even if you change weapons.
-If you don't have a parachute it won't show on your back.

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A small detail:

-For safety reasons CJ will store any necklace under his clothes when he wears the parachute.
-When you're done using the parachute CJ will put the necklace back on.
-Unfortunately, he will forget the necklace if you save the game with a parachute and load it.

Alright, this is just the code's trade-off, but atleast it's realistic.
You wouldn't want a necklace hitting your facing if you were skydiving eather.