Are there actual white markings on the abdomen, or are those merely reflections?

They weren't white marks. There were what looks like indentations. Like little pockmarks. It was all redish brown.

Could it be a false widow spider? I haven't been able to figure out if they are in my area.

Your spider looks very similar to the False Widow, there would have to be other ID keys besides the red hourglass underneath to tell if your topside image is not a true widow. There are other forum members more versed in spiders.

Absolutely the False Black Widow, Steatoda grossa.

Yup, definitely a spider. :)

What? I didn't know there was a false Widow spider. I would have killed it in an instant. We have the real thing here. Black widow spiders and juveniles. If you live in an area that has these spiders, you need to know what the juveniles look like. I have killed at least 60 of them. Thank God I never got bit by one. They love to be between my nursery pots.