My dog (also a rescue) sounds a bit like this - he compulsively runs between the windows and the back door, barks furiously at invisible things outside and paces around the place. He’s obsessive, anxious and gets very agitated if prevented from doing the obsessive behaviour. He also came to me with no reward structure - he didn’t give a shit about food, or toys, or me saying ‘no’. None of it meant anything to him. I find it deeply un-relaxing and stressful, so I can imagine how you’re feeling.
I’ve tried: An adaptil collar, adaptil diffuser, Xylkene, giving him porridge (highly recommended by greyhound owners on the internet. He’s not a greyhound.) Covering windows, curtains, rearranging the furniture, cutting down all of the shrubs in the garden, white noise, shutting doors, baby gates, treats, toys, training sessions, a crate, standing in front of him to block him from getting to the window, lifting him down from the window, time out (for him), time out (for me), shouting (not proud of that), crying (ditto), going to bed at 8.30 and turning off all the lights. Threatening him with sending him back to Spain on the first available ferry.
You may be getting the idea, none of these things have provided a quick and easy fix...
He’s very slowly become easier to live with. I think the adaptil and the Xylkene did chill him out just a little bit. Giving him a bone or a chew is sometimes really successful...but then again sometimes he’s not in the mood, or sometimes that stresses him out and he runs around with it whining. Changing rooms sometimes works - sometimes if I go upstairs to the bedroom he’ll literally flop on the bed and sigh like he’s saying ‘thank God I don’t have to patrol those windows any more.’ On the other hand, sometimes if I move him away he’ll get more and more stressed. He now is often distractable with a toy or a treat, but will then go right back to the window. If he’s VERY tired he doesn’t do it - but I’m talking a whole day of physical or mental exercise. Chopping down the shrubs did really help, because he used to obsessively run backwards and forwards in front of them. On the other hand, covering the windows didn’t work at all - he was furious because he knew the window was still there.
Sorry, this has become a massive essay. The short version, as our trainer says (oh God, the amount of training we’ve done...) is ‘Its very hard, because nothing is as exciting as the obsessive behaviour, he doesn’t want anything you’ve got, and every time he gets to stare out of the window, it’s reinforcing and rewarding to him, but if you stop him he gets so stressed he can’t engage with anything.’