Most RV-use generators (Honda & Yamaha) have fuel cut-off switches and fuel tank vents that seal for storage. Placing smaller generators in a storage container will further reduce fuel smells and provide extra space for accessories; i.e., bike cable and lock, owner's manual, extension cords, adapter plugs, etc. See information on storage containers, below, re-posted from another thread.
Much discussion in other threads regarding the Rubbermaid Action Packer. Read all posts for details on size and where to buy:
Weatherstripping around edge of lid will reduce/eliminate gasoline odors inside your vehicle.