Q: track pad won't click on  login screen

I don't have Yosemite so my help will be limited.  However, you could try re-setting the NVRAM.

https://support.apple.com/en-us/HT204063

This may be a connection problem for your mac during the login. Sometimes the mac, for power reasons, only connects to wireless after the login proceeds. Try resetting the bluetooth settings and look at the trackpad settings in System Preferences. If this does not work, try replacing batteries in your trackpad.

-J

This has bugged  me for years. The workaround has been  to take a mouse with me but it has always mystified me as the trackpad is working when logged in. I found that the suggestion on this page, Step 2, to set the trackpad speed to the midway point has worked.

http://smallbusiness.chron.com/troubleshoot-trackpad-macbook-49263.html

A big thank you to the non-Apple website for this solution. I suspect  it is quite an old post but there are other suggestions too which might work in your case.

Sorry, the trackpad works on the login screen on Restart but it did not work this evening when I started up, eight hours after my last post. Restart is obviously not really Restart, more like Wake Up.