If your government won't abide by the constitutional rights you already have, what makes you think adding another amendment to be ignored would do any good?

Not that a privacy amendment wouldn't be a good idea, but you also need to come up with some way of enforcing compliance upon the government. Since it is the government that is itself supposed to be the agency that enforces your society's laws... you have a problem.

Quis custodiet ipsos custodes? That is: who can guard against the guardians?