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Down load the various FD manuals available from the internet. Foxed.ca - Mazda RX-7 Manuals
Buy a good electrical multi-meter.
Start testing the wiring.
It's a really basic circuit for the headlights. Stock there are 3 wires - low beam 12v, high beam 12v, ground.
You'll have to get a meter and see what's going on. Could be a bad connection, from the picture they cut off the stock plug and wired in their own harness.