Custom page templates not appearing on local install

I’m developing a theme on my Mac using MAMP to handle the local server side of things.

All is fine until I try creating a custom page template. It just won’t appear in the Page Template dropdown. I’ve put my custom template on the live site to test it and it works fine but I can’t figure out why it won’t do so on the local install.

Tried restarting MAMP and my browser and no joy.

Any clues?