Every few days (probably once/twice a week) my Z will make a "clicking" noise when starting and not crank. No indicators. Completely dead. I found that removing the negative from the battery terminal fixes the problem, and the car cranks right up. What could this be?

 

I had a similar problem on my 240sx back in the day. I found out that the terminals that connect to the battery terminals weren't making a proper contact. It's as if the battery was completely dead and couldn't crank the car.

Make sure that all the terminals are completely clean, no oxidation at all (use a steel brush to clean everything if needed) and most importantly, make sure that the terminals are fully seated and properly tightened. Also, once that is done put some dielectric grease on the terminals to prevent formation of corrosion.

I hope that helps.