Success! I have fixed the darned stove.
Here's the scoop, in case anyone else needs to solve the same problem.
First, there are no removable connectors on the thermocouple/valve assemblies. They seem to be a prefab unit -- 2 wires, thermo tip, and fancy valve with solenoid. I saw no way to disconnect the wires so I left them alone and scratched my head
Something the Dickinson
rep said on the phone
stuck with me: "If the valve unit rotates on the manifold and drops away from the cover panel then the knob might not be able to press down far enough to activate the solenoid."
I realised that one of the knobs (the one for the burner which would not stay lit) was leaving scrape marks on the face panel, but the other (for the burner which worked ok) was not. So one knob was bottoming out while the other could be depressed all the way. Hmmm.
I couldn't *see* any difference in the travel. But I threw a couple of small washers over the knob shaft for the afflicted burner. Now the knob stands proud of the panel by about 1/8 inch even when fully depressed.
I reassembled the stove and Ta-Dah! it works perfectly. Both burners auto-ignite *and* stay on w/in a second of being lit. So, here's my inference:
The voltage from the thermo is so small (1.5 mv) that it is not enough to trigger a solenoid to close; but it may be just enough to *keep* a solenoid closed that is already energised. So the knob vertical travel is actuating some kind of slider that not only opens the gas valve but *also* forces the solenoid closed. After just a second or two the thermo heats up and the solenoid will now stay closed even when the actuator is retracted -- by a spring which returns the knob to its normal elevation.
The knob has to go *all the way* to the end of its vertical travel to close the solenoid. Anything short of that -- even a millimetre -- apparently is not enough. This one must have been marginal all along. I could see no evidence that the valve assembly had rotated on the manifold; but if the darned thing ever fails again in the same way, I will know exactly what to look for.
BTW the manifold and valve setup looks intimidatingly fragile, complicated, and precise. I hope it never fails. I would not want to try any parts
swaps on it :-)
I hope this cautionary tale may prove useful to someone someday :-)