I agree with user 10126. Real good advice there.
Rescue dogs will generally suffer from anxiety. They understand when they have something good and get attached very strongly.
Basically you need to train the dog to be left alone.
I assume that you already work with the dog with the basic commands. If not, it's really important you start. It will create a bond, a trust between you, as well as tapping in the dog's natural instincts which is "to work".
Training the dog to be left alone starts in the house:
In one room, teach the dog to sit and stay. Walk a few steps back. If the dog moved or display anxiety, you've gone back too many steps. Work on length of time. Again, if the dog moves, you've waited to long, just go back a step.
Reward when the dog stays as you wanted. Start again and again.
Each time, increase the time and distance.
When ready, move to another room or the edge of the room.
Continue to increase distance and times(like going upstairs or outside with the door open).
Then the same but close doors... for a few seconds then increase time. Continue to reward good and wanted behaviour.
Dogs are very clever, they soon work it out. Plus if you train this way, the dog will think he's being left alone to work. And they love that.
I have rescued a lot of dogs and this has worked on all of them. Training is paramount for trust and understanding. Dogs love to please humans and vice versa.
Historically , dogs are descended from grey wolves. There daily lives are to get up, go hunting, if successful, return to the den and sleep all day. Go out at dusk for possible further hunting then return for more sleep.
Mimicking nature is the best. Get up, walk the dog, feed it, leave it, return home, walk it, feed it, settle for the night.
Dog love routines, it makes them feel secure.