This is a maybe, but could not find a manual for the serial number range but found one close to it.
First it is normal for Mariner and Mercury to use purple as switched power (Key turns power on)
Also uses Tan/Blue as the alarm wire for over temp, low oil pressure, low oil or lube, an others but depends on motor
In the link below I can see where the alarm module (item 3) is powered by the purple wire.coming from a terminal block (item 14). Page 121 or 2D-3
http://162.144.28.33/lib/mercury/manuals/135-150-175-200-225-jet.html#/120
With the wire disconnected will the alarm sound when key is turned to ON, and does it go OFF once motor is started?
If it does the wire might not be needed. If it will not start without it, then there may be an issue with the key switch or circuit.