1999 Buick Century Cooling Fan Control

Thanks for the reply, Jack. Since my first post, I have found that the problem is insufficient output from the coolant temperature sensor. I bought a new one, and removed the old one. I measured both and got 2.8 Kohms cold and 300 ohms at boiling water temperature. They were both OK.
The problem is apparently that the cooling system, at least in that area, is so crudded up that the hot water doesn't get to the temperature sensor. I expected water to come out when I partially removed the sensor, at least until I drained the cooling system, but none came out. Even after the sensor was removed.
The last time I filled the radiator, I noticed that there was no water came out of the air bleeders when I opened them. A major cooling system purging is next on the list.
First time I ever had the cooling fans stop before there was any overheating or cooling system problem that indicated incipient cooling system trouble when the coolant had gelled to that extent.

I had this written up yesterday, but haven't learned how to get around in the forum. It was between my other two messages.
Sorry about the added comments--I wouldn't want the business at hand turn into reminiscences or comment far afield from the subject at hand.
Of course the high cost of automobile maintenance is close to the subject at hand.

Yesterday's message:
I was kind of caught by the donation aspect of the forum. Most car repairs plus parts seem to be in the $300 to $1800 price range these days, at least if doesn't require an engine replacement.
Since a correct diagnosis is probably the the most important part of a repair, it is apparent that they are of no small value. That is you guys (Bob & Ken) area of expertise, and made the question of a donation difficult. $5 would have been an insult, and $500 was out of my range. I didn't know where the line between them was.
Since my question, I tried shorting the ECT sensor output to the sensor ground, and the fans started up. I would have replaced that first, but is so inaccessible that when it showed some output, I didn't check further. When I get one, I will measure its output and if it looks like the problem will proceed with the additional dismantling to replace it. I will send you the temperature versus resistance curve.
A note aside:
As a great depression kid, the cost of auto repair really illustrates the way inflation has changed things. Almost as bad as restaurant menus. In 1940 the transmission on my dad's 1936 Terraplane went out. I went to the nearby auto wrecking yard. The boss told me I could have a transmission for $4 if I took it out. That wasn't difficult, so I went ahead and repaired the 1936 Terraplane. Probably would have cost my dad $100 if I wasn't a DIYer.
A new Terraplane was probably $6-800 then. It was Hudson's low priced model.

Disregard my last diagnosis. The cooling system is not as plugged up as I thought. Apparently a closed thermostat and the radiator cap on prevented water flow.