They look like this
In case anyone else has the same problem, turns out it was the plug
that plugs directly into the fan. I wiggled the plug and the fan would
run as long as I continued to wiggle it.
Mazda made a pigtail for this up until 2001.
Now you will have to search the salvage yards and find someone that is
willing to cut the wiring harness and sell you the plug only.