I forgot to mention that before we had a live-in housesitter, we tried to make things as similar as possible when we were away, as when we were home.
That meant leaving a TV on in a bedroom all night, sometimes for a few nights in a row, regardless of whether we are home.
We also make a point of leaving different bathroom or hallway lights on all night, home or not.
Then, when our now-housesitter would make her stops here, she'd just change things around a bit, same as we would do if we were home.
We also made a point of sometimes leaving the paper out all day/overnight, or leaving some of the (junk) mail in the box overnight, even when we were home, like perhaps we were lazy or sick. (Yup, we can be lazy, even when not sick!)
We've always preferred NOT to "notify" folks such as post office, police, etc., that we'd be away. Loose lips, etc.
GC