Looks like you're long overdue a clam-off refresh in there!
If there's anyone who knows about Elise fans, it's this guy. ^^^I think D3shooter covered how the fans attach in one of his videos, might be a useful reference.
Comparing to the other fan, it kinda looks like a mounting tab may have rusted and broken so you may need to get creative.
They both come on but in series first (so there is a 6V drop across each) then parallel (12V drop across each). DC motor speed is proportional to voltage (if it has enough current to overcome the loads), so this gives it an easy two-speed control.I think I read that one of the two fans comes on first and the second one only comes on if things really heat up.
Does anyone know which fan comes on first? Is it the driver side one or the passenger side one? Actually I was in heavy traffic the other day. It hit about 104 C and then the temps dropped. I scanned LotusTalk and that seems to be the second fan starting up. I am guessing the my 1st fan is the one that fell down and currently doesn't really help out.