300 Fourtrax starting issues.

I recently bought a 88-89 300 , it wouldn’t start unless you crossed it across the solenoid, I bought a new one and installed it.

After I put new solenoid in I went to hook up the battery and as soon as I try to hook up battery it turns over.
Even with key "off". Wont start with key off but turns over , starts right up with key on.

Anyone got any ideas , does it matter which wire goes where on solenoid?

Also trying to find serial #?
Paper tag on front A-frame/fork worn plus has paint on it?
Is there somewhere serial is stamped in?