nikon n70 viewfinder illuminator question

Hello everyone,
is it normal for the viewfinder illuminator(the whole thin orange box) to stay lit even when the power is off?
It stays on no matter what, and goes off only when there are no batteries.

I recently bought the camera and the fresh batteries I put in died after just 16 or so exposures. So I'm guessing there is a leakage somewhere and suspecting this might be the reason.

That's not normal for any camera .
Where the focus point on any camera lights up , it is just briefly as focus is made .
This function can be adjusted how long it is lit for but is always just very brief .
Sounds like your camera has a short .
Sounds like you need to get another .