I've got an intermittent fault with a BMW 1997 Series 5 - 2.3 SE Manual Transmission

Problem summary: I can open the locks ok, when I put the key in the ignition, all the ignition lights come on. When turning the key to the start position nothing happens. Battery tested and is fine. There's no clicking of the starter motor.

After a random / varying amount of time the car will start. So for example, if i leave it for an hour or a day or whatever it will start without me having to do anything.

Any ideas ? The problem is intermittent. If I leave it perhaps an hour or a day the car will run perfectly. The fault will just disappear. When the car runs its perfect.