[Yesterday: 2 miles; today: rest]
I did some more research on our clutch problem with the Toyota truck. It appears that the most likely culprit is the hydraulic master-cylinder, connected to the clutch pedal.
The amount of pressure in the hydraulic line causes the slave cylinder mounted down at the transmission to actuate the clutch against a heavy spring. Our problem is, if the clutch pedal is held down, the initial strong actuation gets weaker and the clutch starts to engage. So it is most probably a leak in the system inside the master cylinder.
I’ve ordered replacements for both the master cylinder and the slave.