FM12 isn't supported for El Capitan.
In these cases I've found that the most reliable correction was a complete uninstall (including deleting the prefs files) and then reinstalling and updating to the latest version.
Thank you so much Mike for your suggestion. I was very close to uninstalling, but just before doing that I happened to play a bit with windows, split view, etc... while FileMaker was open. Suddenly, without any apparent reason, I noticed that the inspector had reappeared (it was turned don, but invisible to me).
I hope this doesn't happen again, but I take it must be some sort of glitch related to el Capitain.