I assume it’s the same mechanical regulator used on the later K5, you can pop the lid off these and check for continuity. The rectifier is solid state and if you put your meter onto the ohms setting, then measure between each set of the leads they should read a high resistance one way and lower when you reverse the meter leads. Don’t get too hung up about the readings, you will find the high readings will be consistently high and the lower readings similarly low. If they all read low in both directions then the rectifier is defunct. It will usually burn out the wire as the battery voltage can go straight to earth and is not protected by the fuse. A combined solid state reg/rectifier can be bought pretty cheap and perform better than the original.
