Radiator fan not starting on its own

I have a Mazda 626, 1989, the mileage I don't know, but must be a lot. The engine size I believe is 2.2

The problem is that it overheats because the radiator fan does not start when it's hot. The coolant sensor was just replaced and it's still the same.

If we push the fan to make it start, then it keeps going and cools OK.

I'm not sure if it's juts a mechanical thing like the fan being not lubricated enough and there's some resistance to start moving or if it could be that the cables that connect to the coolant sensor could be responsible. They look pretty old indeed.

What do you think? Thanks!