This is Trooper. I'm still learning his language. Last night he walked into the hallway and peed all over the floor. As soon as he did it I realized that he had been trying to get my attention a few minutes before and I ignored him. Trooper is training me to understand him, but I'm a little slow - especially when I'm focused on food.
Trooper was run over by a car and lost his leg. His owners dumped him at the vet and never came back. We were supposed to be his fosters, but couldn't stand to get rid of him.
I have found that having set times for walkies helps, but I also observe. When my dog starts pacing around in tight circles, as if she is worried about something, I take her for a brief walkie and she goes. But the next scheduled walkie has to happen at the set time, regardless of how recently the unscheduled walkie occurred. That way, she knows when she is expected to do her business, always. She doesn’t do the pacing in circles thing very often. They really do want to please us, but like you said, it’s learning to speak their language. Trooper sounds like a real Trooper. Perhaps the person who left him at the vet couldn’t afford to pay the vet bill! I don’t know how people can just abandon an animal like that.
Try using a bell. There are three small bells (light weight Christmas decoration types) hanging from door knobs in the house. When I was training our dog, I would ring the bell then put her outside until she went potty. If I had time, I would make her ring it by running her nose into it. She’s not the brightest dog I’ve owned, but it only took a month or so for her to catch on. In addition to going potty, she now rings it lightly or gestures towards it if she wants food or to chase a cat outside.