I got a 97 Mercury Cougar that when I start it it stays
engaged and keeps wanting to start unless I move to key
back just a little bit so far. Burned up two starters plus I put
a new key ignition in and it still does the same at one point
or at some time it would engage on its own while the car is
cranked that's what made me replace the key ignition
Just to be clear, was it the ignition SWITCH or the ignition LOCK CYLINDER you replaced? They are two separate things. The switch is where I would start trouble shooting.