Mazda 3 2005 unknown cable

This cable may belong nowhere because it's meant for a feature that your car doesn't have. Wiring looms come pre-assembled, typically manufacturers make one that works for all or most models of a vehicle rather than having one custom to a specific set of features, so it's not unusual to find a cable that doesn't do anything. Of course it could be something important, so you're right to trace it.

I'd suggest testing the pins with a multimeter to see if they have power, if not you can look at which fuse slots are not filled. If it does have power then you can try pulling fuses until the power drops, then you know what it's for. Wires with alligator clips on each end are great for this kind of work, you clip one end to one of the multimeter ends and the other to one of the pins on the connector, saves you having to fiddle around each time.

Is the car giving any engine codes? That looks like a sensor connector (ECT, maybe?) - but if an engine sensor is left unconnected, it's usually going to give an error code.

As others have said it probably leads to nothing if there are no error codes. Do you have a multimeter? if so do a continuity check to these wires and the fuse box until you get a hit. Then you will know exactly what it is.