Before just replacing the rectifier you need to test the stator. Remove the rectifier cover, Separate the stator yellow and yellow gray connector. Connect a ohmmeter lead to each lead. It should show 0.12 +- .07 ohm. If it doesn't replace the stator. Then check for a grounded condition. Connect one lead to a clean ground on the block then to each lead, either lead should show a high reading, if it doesn't check the wiring because the stator or its leads are grounded.To check the rectifier, you really need a carbon pile load tester. You also need to run the motor at 4500 rpms which can be a issue unless you have a tank or a engine dynomometer. First to check the rectifier is getting power disconnect the purple lead connector. Check the voltage at the lead with the key switch in the ON position. If its not showing full battery voltage there is a wiring problem in between the switch and the rectifier.
The tach gets the RPM reading from the stator through the rectifier. So the tach won't work if either is bad. The rectifier is much easier and cheaper to replace, so I would start with that. You usually need to remove the leads to get accurate readings on the stator (see the specs above). You should also have a voltage regulator (or combo rectifier) if you have the 35 amp stator setup.