Mystery of misbehaving hose bibs and missing shutoffs
The hose-bib on the west side of the house is now working. I'm not 100% certain why or how, but it seems likely that @Tyson was on the right track with his obstruction theory.

I went outside this morning with some old coat hanger wire to try probing the bib for obstructions (like the Mud Dauber wasp nest suggested by Tyson).  However, before using the wire, I removed the divider from the bib, checked it for obstructions without finding any, then felt around the inside of the bib with a finger, dislodging some crusty material (a bit like limescale) with an accompanying trickle of water.  When I then turned on the bib, I got normal flow.

The only odd thing is -- I performed exactly these same steps when troubleshooting after the problem first occurred on Friday, but with no effect.

But hey, I'll take it.  Problem solved for now -- without a potentially embarrassing, unneeded service call to a plumber.  I'll give whoever ends up buying Dad's place a heads up in the form of a "things to keep an eye on" list.

Thanks again to everyone.