This morning I did the test described in the workshop manual. The pump failed. The ball on the larger-diameter side is not sealing.
I decided to try and fix the pump using the method we first used in Germany and described in the workshop manual (using a punch to smartly hit the ball to form a seat in the brass body). I'm embarrassed to say that I could only remove the square bolt on the small side. The bolt on the large side is so tight that the wrench rounded the corners.
I inspected the seat on the small side. Even though it seemed to be sealing, the seat is not evenly formed around the hole. I have declared the oil pump to be trash and will order a new one from LaNelle on Tuesday. (She doesn't open on Monday.)
In the meantime the bike has another challenge that may have contributed to the breakdown by lowering the oil level in the primary case. There is a crack in the aluminum where the primary chain adjuster threads into the primary case. It results in a drop of oil falling about every half-hour. I've been told by some blokes at LaNelle's that it's not an "unheard-of" problem. They referred me to a fellow whom they say is an artist with a Tig welder and can fix it "better than new." I like "better than new!"
Next, I'll learn whether I only need rings or pistons as well. Would anyone like to offer an opinion? Stock Triumph or after-market? Keep in mind that "better than new" is preferred.

I still need to learn where the aluminum chips in the oil came from and address that as well.
It looks like the "School of Hard Knocks" tuition has been increased by several hundred dollars. I don't like it but I refuse to cut corners on rebuilding a Bonneville. Every day we have fewer of them.
Thanks, Y'all!
Al