GTA 5 Mission 12 starts if you choose Smart heist approach at the end of mission “Casing the Jewel Store”.
Steal and deliver a Bugstars van
When you get to Elysian Island, and hangar with Bugstars van inside, get to the rear entrance, the one that is looking at the water, and enter the hangar on foot.
There is only one worker behind the van. Silently approach and kill him (you can use a stealth mode). Drive the van to the back. This approach will not cause an alarm, and task “Sneaky Pest” can be completed.