Driver's side, behind the rear axle, up before the bumper. It's about the size of a lunchbox with rubber hoses going into it.

I assume at one point mine had a metal box or something around it but most has rusted away.

What is it and how best to keep it hanging where it is?

Will

 

What you described sounds like the EVAP system charcoal canister. It is mounted to a bracket.

 

best way to keep it hanging?

go to a junkyard and pull one from a vehicle that has what you are looking for. use the existing holes and brakettry FTW!