Albea, I don't think you're eccentric about having a concern for your pet while you are absent from the house. I think you're being responsible & loving. I agree with jackiesdaisy's ideas for ensuring pet safety when you're not at home. We have a large, weatherproof verandah room along the back of the house. A short flight of steps leads into a little fenced (open wire) courtyard.
Our dogs stay in this verandah room when they are home alone. They can go thro' a doggy door & down into the little courtyard...to go to the toilet & to be seen by anyone who comes to the side or back of the house. I like jackiesdaisy's idea of putting a sign on the house telling the number of pets inside. In our case, one pet could huddle in fright under the day sofa on the verandah. So it would be good for anybody saving them to know the number of pets there. We'll now put up a sign. Thanks for sharing this idea.