Tach sender wire will have a AC voltage on it. The tach will count the pulses and convert to dial reading. if the rectifier is shorted to ground, the tach operation can be affected.
88 mariner 75hp 3cyl. i was testing the grey wire. wife wanted to go on the river and when i hit a wave the tach started working. when I turned the engine off the tach got stuck at 2000. Friend gave me a new tach today. will try it and repost
It is not unusual for the tach to stay at the last reading it had, when power was cut off. It should zero when it gets power again. If not, the tach or it's wiing harness is likely suspect.