The correct answer is B) The amount of the error and the sign will generally be the same on all headings. This is correct because gyrocompass errors are typically caused by factors such as latitude, temperature, and the ship's motion, which affect the gyrocompass consistently regardless of the ship's heading. As a result, the amount and sign (E or W) of the gyrocompass error will generally remain the same across different headings. The other options are incorrect because A) the error shown on the repeater may differ from the master compass due to factors like signal transmission, C) the sign of the error can change with heading due to the nature of gyrocompass errors, and D) the error is not necessarily constant and can change if the compass is stopped and restarted.