I know you said you have a new dash cluster so it's obvious you have been moving/disturbing the harness and associated connections. I want to confirm of a few things first. Do the lights stay on with the ignition key off and the light switch off? There are a few other lights on this circuit, some are options but if you have them (working ash tray light, Clock light, Tach light and steering column shift indicator light) are they also stuck on? What you have is probably a short but a faulty headlight switch or a short in your wiring harness or your new cluster could also be the cause. Everything is suspect. We have to start somewhere. If you look at the drawing you can follow a few thing that happen.
1. Constant battery is applied to the headlight switch on the Black/Tracer wire (Black-TR on the drawing)
2. When the headlight is turned on, power leaves the headlight switch on a Black wire which goes to the dimmer switch, marked "panel light switch" on the drawing.
3. Power leaves the dimmer switch on the tan wire and goes to one side of the fuse.
4. From the other side of the fuse, power is delivered to the cluster on an orange wire, to pin #1 of the round cluster connector.
If your lights are on all the time, you have power on pin #1 of the dash cluster connector at all times and that is wrong.
You need to get a test light to verify voltages at the points that will be tested. I would work backwards starting at pin #1 of the cluster connector. Check it first with the connector attached to the printed circuit board. I'm sure you will have 12V at that point but test everything and assume nothing. Next, gently pull the round connector off the cluster and check pin #1 again.
If you feel comfortable, continue testing back. If not, post what you find and we'll go from there.