Found my dads original 1971 duster!

Could one issue cause all of these not to work?
Yes its possible, but probably not a harness problem, but a bench test problem
Also, I don’t have the cluster or dash installed, I just have it sitting on a towel on the steering column.

I’m seeing a lot of stuff online about bad grounds.
There's a lot garbage online too. Since you want to bench test, you will have to make sure the circuits have a return to the power source. Your challenge will be to understand each circuit you are testing. The horn uses a relay. When you look at the circuit, I suspect you'll see the horn doesn't work because either the circuit to trigger the relay or the circuit tp power the horns is incomplete. Maybe both.

You don’t think it could be the dimmer switch then?
My goal here is for you to decide that yourself if that makes sense. ie. The best thing I can do is help you learn.
Go back to the diagram and follow the path to the headlights, and then to the hi/lo switch. (I didn't include it in the main circuit drawing, but you can draw it in). Then follow the path to the parking lights. Finally follow the path to the turn signals.
My actual headlight switch is new as well. But this black wire was hanging beside it. Not sure if it should be pushed into the harness or pushed onto the tab on the switch.
Look at that terminal and compare it to the proper terminals. I don't know what that wire is yet, but doubt it will stay in the connector.
Look in the service manual and you will see which wires go in which cavity. Also on the headlight switch, the terminals are labelled. The terminal labels are often a little different than the wire codes in the manual. For example. B on the headlight switch tells us that terminal connects to 'Battery' power. ('Battery' used this way just means system power.) For the headlights wire L1 (black with tracer) connects to terminal B1. L(some other number) connects to terminal H and goes to the high lo switch.
You can do a search on FABO for more examples in color. But even so, the diagrams in the shop manual are your friend and guide.
While its nice to test every circuit on the bench, it may not be practical. It may be more practical to check the wire position and terminal retention and condition at all of the connectors. Any splices in line make use of flexible shrink tubing, etc. There's threads here (FABO) about splices and crimping open barrel terminals which may be helpful.