You didn't state the year of that 90hp, however, the answer to your question is "yes".
Black = Ground lead. To tachometer ground (G) terminal.
Gray = Signal lead from rectifier. Attaches to tachometer sensor (S) terminal.
Purple = 12v source, hot only when key is in the RUN or START position. To tachometer voltage terminal (B), (+), whatever it may be marked.
That engine will have a solid state ignition system (Magneto Capacitance Discharge), meaning it is a solid state ignition system but self contained, supplied by AC power generated by the stator under the flywheel (keeping it simple).
As such, you willl need a tachometer that operates off of the engine's alternator charging system. It usually has a dial on the back that you set to a specific number.... on your engine, set it to number six (6).
The above assumes that your engine is indeed a "Magneto Capacitance Discharge" ignition model... anything after 1973.