Yup,
Unloaded is a no brainer, it doesn't need a trigger lock if its stored in a locked gun cabinet, or if its locked in a closed off closet, or even locked in a case and kept out of view, but since its locked up and unloaded its pretty useless for home defense, so most go above and beyond the min requirements. Mine are trigger locked, in a locked gun cabinet, with ammo in locked boxes in a separate room.
The min requirement is guns and ammo stored separate, and gun either trigger locked, or locked away (you may get away with removing the bolt or other vital component and storing separate instead of locking).