Seems to be the lens. The mechanism in the body moves. If I press the DoF lever, the aperture closes and stays closed. If I press the shutter, there is no movement of the aperture, whether open or closed by me using the DoF lever.

I'm thinking you're theory about it being gunked up is correct. I don't think it is a body problem. Off the body, pressing and releasing the pin on the lens does nothing. Time for a CLA, for a start, I guess.