Cooling fan confusion.

I have a 59 Corsa D 1.4 and it overheated, I found the fan had not cut in, fuse checked ok temp sender on thermostat looked in a poor state and could not get a reading across contacts when hot so replaced it.
No improvement so checked power supply across temp sender lead and got 5 volts. Checked voltage supplying fan when hot, nothing. linked lead to sender unit , fan came on and ran and ran.! Still ran with ignition key out and in my hand.! Could only stop it by pulling plug off fan.
Went in for lunch totally confused, after lunch went back to car replaced plug onto fan, silence, started car plugged in obd meter watched temp rise to 205 degrees and fan cut in , ran a few moments to cool car and then cut out, and behaved as it should for now. WHY ?
I am quite prepared to replace all parts involved if I know what they are and Where they are. Can anyone help please.?