Drew collier , Not positive but could be the wires for charging/starting system. I will post a link to schematic for Protege for you to reference the color of wires from to see exactly what they are for. 2nd link is to be for a downloadable service manual with schematics also just scroll down to Service Manual (PDF) [50MB] download at your own risk. The wire possibly got hot and melted due to a short, wire insulation may have deteriorated, mouse/animal may have chewed on them, if you had to turn/crank engine over excessively(too long) wires could melt, etc. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
https://www.scribd.com/doc/58941318/Mazd...
http://www.floptical.net/mazda/
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Drew collier post some images of your wiring harness. You did not tell us from where the harness comes and where it goes. It is difficult to identify it and anything at this point will be a guess. Use this guide Adding images to an existing question to post some images. you also want to tell us what year your Mazda is and what engine size as well as transmission type (AT/MT)
crwdns2934271:0crwdnd2934271:0 oldturkey03 crwdne2934271:0
Its a 1999 with a 1.6 and a MT
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Drew collier give us a better picture of the wires entering the connector. That may help determining which wire is what.
crwdns2934271:0crwdnd2934271:0 oldturkey03 crwdne2934271:0