Q: How do you change the SIM card on an iPad Air 2?

You can use a paper clip just fine.

Remove the SIM card from your iPhone or iPad - Apple Support

Apparently not. The SIM tray won't eject.

Make sure you give a firm push.  The actual removal tool is nothing more than a glorified paper clip.  It really does nothing other than push in the hole.

Thank you Phil0124. That did the trick.