those thermos are designed to run in an interesting way.
low speed, two fans run in a series circuit. high speed, fans run in parallel. This means that when warm both fans should run no matter what. If one fan has failed then neither will run untill the overheat condition triggers parallel mode, then one will start. That mode is also triggered by air con.
Basically if there are fans running at the lower end of the normal temp scale then you shouldn't have any problems. Just have a look with the bonnet open. Yous should be able to hear them too.
1987 Jaguar Sovereign - Metallic Green
3.6L DOHC 24 Valve