Yeah, I tried pulling on the cables and pushing the connector in - it
doesn't make a difference at all. The engine gets unhappy when I rotate
the injector. Just this one; not the other three.

Thanks.

What's inside an injector, anyway - is it just a solenoid valve?

Wiggling the injector shouldnt affect fuel flow and prolly wont move
dirt.  what it WOULD affect is the electrical connection.

look closer and wiggle softer at the harness and connection.

Just sayin' check the obvious first... if moving the actual connector
affects then it's either in that connector or the injector pins/winding
solder joint

Yes, a valve under the cap.

Poking about today, I find that one of the injectors on my wagon is
apparently the root cause of my once-in-a-while
running-on-three-cylinders symptom. If I wiggle that injector while the
engine is running, the engine goes erratic. Wiggling the others causes
no symptom.

I did recently let the car run almost dry and I'm wondering if some
floating crud got in the fuel lines and made it into this injector.
Would like to take out that injector and clean it. How do I remove the
fuel rail, though? Feels like the injectors are held in just by O-rings
and should just pull out - but then there's the minor detail of
relieving fuel pressure. There's a screw-on plastic cap at the inlet
end of the fuel rail; is there a valve under that or will unscrewing it
squirt gas everywhere?

tia..