1991 Buick Century

That view is looking under the hood, passenger side, coolant temp sensor-- fan relay, 3.3litre.

Can you check for codes? On some of these older systems, if you turn on the ac, engine running, the fan starts. If you unplug the cts, then start the vehicle, the fan takes off. If you use a jumper A&B terminal of aldl, key on, no crank, the fan will take off. I don't have your wiring info right in front of me, I do have a GM vehicle similar to yours, different model and engine, the above info will cause my fan to run. You need to check wiring circuits before replacing anything.

I just wanted to add, as far as sensor and relays, at the connector, I match the wiring colors with the diagram, to make sure I have the correct connector.