I do not leave the key nearby. My swim suit has a pocket with a velcro'd flap and that is all inside the wetsuit. All trucks I have used there had old style metal keys, not key fobs, so this makes diving with your key easy.
Also leave the windows partially open so people passing by know its unlocked.
BEWARE of credit card insurance for truck rental. Nearly all insure CARS, not trucks! I use American Express Premium insurance. MUCH lower cost than getting insurance from the truck rental company. Its usually under $30 for your whole trip, not a daily fee. And its easy to use. You sign up with your card. There is no charge unless you rent a car/truck with that card then it automatically kicks in.