Your AE-1 is an entirely different beast to the brute that is the 1N!
The 1N does not use a screw-in shutter release cable like the AE-1 — that is, not directly into the shutter button. The 1N has a different approach (an electronic one). On the right hand side below the palm door is a socket (usually covered with a cap). If a cap is on their, unscrew it. Canon's Remote Switch 60T3 plugs into here. It can be bought around $60.00 or used ones can be had for around half that.
Now the other trick. If you have a traditional shutter release cable (like the one you might have for the AE-1), Canon has a Cable Release Adaptor T3. On one end is the male plug that matches the socket on the camera side. On the other end is an open socket into which a traditional (plunger-type) cable release screws. There is just one small problem: this gizmo is quite hard to find now so a scout around a Canon dealer or pro-second hand dealer might turn up something.
Download the instruction manual (from mir.com.my/ eos site Malaysia) here.
(This is a
3.3Mb file covering the EOS 1N and EOS 1N RS, the high drive speed pellicle-mirror version).
On the same site (you'll have a ball coming to grips... sorry for the pun ... with the 1N here!), look up Custom Functions. In the absence of a cable release you can have the camera start with a 2 second or 10 second delay, which allows you to press the shutter then get your paws away, the camera to steady and then fire. But make sure you read the Custom functions and how to Clear/reset the camera; sometimes there may be combinations of settings that could confuse a new user and lead them to think something is wrong, but actually it is more often than not only the camera behaving as per a custom function. Enjoy.