Car keys off but fuse still lights up the tester when set to ground

So normally when you want to test your fuses, you set the car to on and put the tester clip to ground then put the tester’s lead on the fuse. if it lights up then the fuse is working. Well, even when I remove the car key, the tester light still comes on. This seems to indicate a short somewhere. Also when I measure the current with a multimeter by disconnecting the negative lead on the battery, it shows about .8A with the car off. Also, when I reconnect the negative lead to the battery, sometimes it activates the car like it would drive the radiator fan for a second or some other electrical parts. There’s also loud clicking noise like the starter is engaging but only for a second. Does anyone know what’s going on?