Take it to a shop. It's the only way to make it look right. The tint film won't work on our taillights because of the curves and angles. I used to have an IS350 that I tried the tint film on, it looked "ok" but not great. That taillight had way less curve than the FX's and the film still came with relief cuts all over it to fit which lead to seams. I had it sprayed later on and it looked 10x better. The FX, I have no idea how you could even do film on it. I had mine professionally painted.
If you try to use the spray paint, it will look horrible. I've never seen a DIY taillight tint spray that actually looked good. It will be uneven, the sheen will be off, it will have overspray, or any number of other problems. Spray paint isn't great for tinting things because by it's nature, it's hard to put on evenly which is sort of required for a tint since you can see through it. It may look ok in pictures, but in real life it will look really, really bad.