Engine bay cooling Fan comes on with ignition

I agree about Roverlike..is he Batman?
And your second premise is also very plausible...I wonder if a link wire could test that theory out...and then you would be Robin...

That is all it would take to verify. The sensor on later cars is a magnet acting on a reed switch, a go/no go system, or as far as I recall. Whether a Pscan could sort the required update I wouldn’t like to say, obviously a T4 will.
M
As an afterthought; the correct header tank & sensor is devilishly expensive & the likelihood of dropping on an eBay listing is a bit slim, you might consider buying a bog standard tank & fit a float switch.
If I recall it was David who inspired me to follow his example. I’ve moved on to a different system now but I’d like to bet my original tank & switch will still be in stores.
If after the system is proven & your up for the next move, would you like me to dig it out, we might come to a mutually satisfactory arrangement.
M

In case of MEMS 3 engine bay air temperature sensor is connected to small engine ECU connector pin 71

 

and bigger engine ECU connectors pin 21 and 37. Same wire goes to pin 37 and above mentioned pin 71

 

My suggestion would be to check what is connected to these pins (what wire colours, are they just looped, check continuity).