The engine light is activated by the overheat switch closing at approximately 247F and grounding the signal wire for the temperature gauge. The actual sender for said gauge swings between 74 ohm when engine is cold and 9.7 ohms when engine is hot. Basically the hotter the engine gets the lower the resistance in the signal wire and the higher the gauge reads, when the overheat switch kicks in the resistance in the signal wire drops to nothing and thus the gauge starts reading as high as it can get.
The gauge itself does not trigger the actual red "engine" light, and neither does the overheat switch. The light's operation is handled entirely by a little circuit board called "engine warning indicator module", it monitors resistance in both the temperature gauge signal wire and the oil pressure gauge signal wire. Why said module is needed, well cause a simple light bulb can't respond to two opposite signal patterns, and oil pressure gauge apparently works exactly the opposite of the temperature gauge - the switch for it is open when there is no oil pressure and closes and grounds the signal wire during normal operating conditions. In other words the lower the pressure the higher the resistance, and the higher the pressure the lower the resistance - and if you were to unplug the switch wire altogether that would read as infinite resistance and suggest no oil pressure, say hello to a brightly-lit red "engine" light.
In case anyone is wondering, the warning module can be removed without adversely affecting either gauge's operation - this is because it doesn't intercept the gauges' signals, but rather it piggybacks to them, in other words the warning module is wired in parallel with both the coolant temperature gauge and oil pressure gauge. If you were to remove the module the temp gauge will still peg up when engine overheats and oil pressure gauge will still peg down when pressure drops way too low, you just won't have the red "engine" light coming on.
Another important note, the module will work properly even if you've ditched the factory pressure switch and are now running a sender with the gauge circuit board resistor jumped (or alternatively, in case of bricks, you've switched to a complete '87 gauge cluster).