Tach hook up on mercury 40 hp outboard?

Hi guys I have a 40 hp 4 stroke mercury outboard that I’m wondering if I can hook up a tach on. This model is a 2006 and doesn’t have electric start or a rectifier. I know most cases people use the grey wire coming from the rectifier. In my case I don’t have a rectifier. I found a grey wire coming out of the computer would that be the wire I need to use for the tach signal wire? Will the gauge need to be grounded to the outboard engine ? Also I have a battery in the boat for now to get power to the tach to run it. Anyone know of this will work or will I need to get a rectifier I installed first?

thanks for any help