Mercury-Mariner, don't know the differences other than color, decals, and country of origin...US/Belgium vs Japan.
On/in the Mercury engine you have a tan/blue strip wire on Pin 3 in the 8 pin wiring harness to the control box and helm station. If you ground that wire, and have the key somewhere other than off, you will have applied 12v across the warning device...horn and it sounds, and if a dash light is connected at the helm station pigtail, it will illuminate.
In the engine ground comes from 3 sources: (1)OT switch on the rear of the block, buried in the water jacket cover, lower left corner, tan wire. (2) Oil level in the oil tank blue wires, shorted to ground if oil level is low. If tank is removed, then the blue wire pigtailing in the engine side of the engine to remote 8 pin connection should be removed from the multiple pigtail.....which also contains the OT signal mentioned. (3) on some engines, a modulation module is installed and it gets the warning signals but modulates the oil alarm to a 10101010 rather than a 0 (solid ground) to identify the source of the alarm as oil level related.
The wiring diagram for 1996 year-model Mercury engines shows a module to be installed. The blue wires from the tank enter and a tan wire exits to a terminal block where the OT tan wire is also located in parallel.....either signal therefore will determine the ground (or not) configuration of the output wire of that junction block which is a tan/lt blue striped wire going to the engine side of Pin 3 of the 8 pin remote connector.
On what the removal process you described i have no idea, but grounding of pin 3, however that is accomplished will blow the horn.
The OT sensor is normally open circuited. At about 195F it closes and grounds the low side of the horn. If your oil tank removal action removed the blue wires feeding pin 3, then the only thing feeding Pin 3 is OT alarm and you must have a malfunctioning OT sensor switch, or a very real OT problem.
Tell Tale water from that engine comes from the exhaust water jacket......follow the hose, not the block internal and is NOT controlled by the thermostat nor higher rpm Pop Off valve. Therefore you could have a thermostat sticking shut, or a stuck Pop Off causing an over heat condition with the Pee being somewhat warm.