Nathan, bear with me on this, I have a Mk 2 manual (basic - no electrics) and a Mk 2.5 Mazda wiring manual, so some exploration is required I’ afraid. On the Mk2.5, all wiring in main looms is complete, wiring between looms is not. These links are the options fitted to some models.
As (I suspect) looms between Mk2 and Mk2.5 are more or less the same, with the same colour codes for individual circuits. then I’m suggesting you take this route, and see if I’m right - or wrong.
First thing - see if there’s a fuse labelled ‘F FOG’ in the lower dash fuse box (drivers side)- should be a 15 amp fuse fitted. If fitted, the wire from this is a White/Red. This leads to the coil circuit of the relay you have, with a switched negative needed for the other end of the coil. This fuse mentioned is fed direct from the TNS relay, which is on when other lighting is selected. - As you say, this will put your added relay on when headlights are on, parking or otherwise. ( Don’t drive with fogs on and no fog btw, it’s illegal.) If the F FOG fuse is fitted then the relay base should also be there, problem is to find it, on my location drawing, it’s at the side of other relay bases, all concerned with front and rear fog lighting. Again, under the dash, and possibly to the right side of the steering wheel. You’ll need a Mazda relay to fit, if you are using one from elsewhere it may not.
If there is NO F FOG fuse, then you may need to tap onto the output from the TNS relay, that’s under the bonnet, slightly forward of the main fuse box (switch the lights on, and hear it click to locate it.) The outgoing wire from the TNS relay should be Yellow/Green - if I’m right, - you can pick your fog relay coil feed from this, you need to piggy-back it. Your relay feed wire will need a 15 amp fuse in it, by the way, for both coil and contact.
If wire colours are different, and there’s no F FOG fuse in the dash fusebox, then if you locate the TNS relay, you need to determine which is the outgoing wire you need to connect to, Sneaky trick I used to use on low volt systems,- you’ll need a multi-meter by the way -_ is stick a pin in where you think the wire connection needed may be, and connect the meter between it and ground (Body) Now switch the lighting on, and if it’s the right wire, the meter should read 12v or thereabouts, The pin won’t damage the wire inside, but if you push it right through the center, you’ll be certain it’s making contact with the wire and not the sleeving. - Just make sure neither end of the pin or the meter clamp touches car body - or wham, you’ll lose a fuse for sure, - That’s a 30 amp one, located in the main fuse box (Under the bonnet) BTNI I think. This is a case of trial and error. I’d stick your fog relay close to this if you can.
If this is totally wrong, then I apologise, just trying to help is all.