Thank you for the advice, folks. I appreciate it. I read the messages (and other ones on the board), I watched the recommended video, and I took the advice to the pool.
At the pool today, I did that buoyancy test. As I knew, I'm not an automatic sinker. (I suspect I was when I was a child, but not now.) As with you, CoachStuartMcDougal, at about 50% or so of air expelled, I started to sink.
I practiced, among other things, gliding then rolling for air. The problem was that when I tried to breathe, I got inconsistent results. Sometimes I could take a few breaths. Other times, I'd exhale for the breath then my mouth would sink beneath the water, and not reemerge until I broke form to grab a breath any way I could.
I am going to have to develop a balance. If I try to breathe naturally, I tend to sink. If I try to keep from sinking, I tend to hold my breath and take shallow breaths.
I also read Nicodemus's thread about one length to one mile, before posting my first message. The problem is that, again, it seems to be those short, shallow breaths that keep my mouth out of the water. When I try to breathe naturally, I sink.
I know it can be done, for other people do it. It's just a matter of learning how to do so myself.