I have a small black wire by the starter with a black box on it. I can't figure out where it goes.

 

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Just connect is back to any source that is bare metal as it may need to be grounded for best operation.
From the picture it looks like the ground to the starter was serviced? ( and a poor DIY job at that! ) That person that did the service in that area may have neglected to reconnect that wire to that ground location.

 

That was me. I had a problem with the nut on the thru bolt. I just haven't cleaned it up yet. I hadn't driven that one in 6 years. Just getting it back on the road.

 

Thanks for the information.

 

Well it was not that bad for a ground cable that IMHO most Mazda don't have enough of them!

 

That looks like a capacitor to me. 3mm wire is not a grounding cable. Anyway yes just bolt it to a good earth. Who knows why it's there but it must do something.