my 2 year old is happy to stay in the bath FOREVER playing with his toys and I just don't have the time to sit in the bathroom twiddling my thumbs for an hour every day. We have always lived in a one story setup; for example at my mom's house the bathroom is at the end of a short hallway, and the other end opens onto the living room/kitchen, with the bedrooms in between.
It's a pretty small house. So you can pretty much be anywhere in the house and still keep him in direct eyesight or close to it. Plus, he's pretty noisy since he likes to take his action figures in the tub and they seem to do a lot of fighting or something lol. So if it gets quiet and I'm in one of the bedrooms and can't see him directly, I will holler and he will holler back and we're good to go.
I do usually check on him every couple minutes in between throwing laundry in the wash, opening mail, laying out pajamas etc. but that is more because he gets water everywhere.
To directly answer the OP's question, I started leaving ds for VERY short periods (like to quickly turn off the stove or get his pajamas out) around 16 months, but I would not be comfortable leaving a 13 month old for more than the time it takes to grab a towel or a diaper or something. Ds was still pretty unsteady on his feet at 13 months and still liked to try to stand up in the tub.