I was having the same issues with clicking, but the rest of the trackpad gestures seemed fine. Removed battery and inspected, seemed fine. Put it back and did a PRAM and SMC reset. Still no result. Used an external mouse and still no click. Tried many forced shut downs and restarts, that just gave me boot issues. So I booted up one last time before giving up and tried to navigate my way to trackpad preferences using right click and the keyboard tab key. I right clicked (aka two finger clicked, TFC from here on for convenience) the apple icon on the left side of the top task bar and TFC system preferences. Type trackpad into the search and hit enter.
When the trackpad options opened all of a sudden the click just started to work again. I can't explain how or why, maybe someone can enlighten me? I updated to Sierra not too long ago, might the system preferences have been reset?
But yeah maybe try this as the first intervention before getting into the heavier stuff because it was a remarkably simple fix. Trust me to be predicting the worst possible outcome! Glad its working again in any case, I was about to lose it!
Be happy to hear if it works for anyone else :)