Buy some pet screening, cut it and staple it in place where you need it. It's very durable and tough to rip. HD or Lowe's .
or cut some pieces of plywood to build an interior separator between the outside and underbed area.
I once made the underbed area only accessible from inside the TT. The outside storage area was only accessible from the outside.
Personally, i got out of the habit of leaving those doors open because the rain spouts allowed water to drip ( or flow) onto he open lids that i sometimes forgot to close. The opened door let the water in. (especially the one on the drivers side) :S