My Datsun is a 1971 240z coupe.

Well how do you fix it if it does move like you said

Does the '71 240 have power brakes? What your car is doing sounds suspiciously like what happens when the power booster has a vacuum leak in the internal diaphragm.

Not for sure, i didnt get a chance to work on the car this weekend.

All S30s have power brakes.

Then I would certainly look at that booster. First make sure it's getting vacuum, then check to see if there's a hissing sound when the brakes are being applied.