You are using + and - for terminals 1 and 2 and that is okay as long as 1 goes to one and 2 goes to two..the second chart is incorect....the first wiring should be correct..the black box you have below the tanks sending unit..what does that represent...?? This should be the sending unit going to ground....as the tank is full in this confition, the guage will read full as you indicate in your test. Using the trouble shooting chart above you can test each leg of the resistor by grounding or open by just lifting the wire off the terminal, through the wiper on the reisitor...as posted in picture by Tom T.
Do not depend on the tank itself being a good ground connection..you can run an alternate ground wire to the frame of the car..please keep in mind here also that the lower part of the sending unit, the bulge that the reistor fits into is the ground point mechanically for the wiper..the sender has a gasket between it and the tank and internally between the bulge and the top cap where the terminals are..you can take a short piece of wire and place it between the sender and the tank with the gasket under the wirre and bolt it down..this wire can now go to your car body and ground ensuring a good connection at this point..seriously sounds like ground is your problem.
In regard to your reducer..if this is one of the type that bolt in and not electronic or bi-metal style as built into your guage..the load will not be enough to reduce you voltage..they work well on larger load device but WILL still surge on first power then fall back. What voltage are you reading on the guage side of the reducer with the ign switch on? Can you post a pic of your reducer...?
Again, the guage will work without the reducer as the guage itself has a built in 5 volt bi-metal regualtor.
The ground is the one most common problen to these guages not working. As indicated in earlier post and pictures above..the wiper, arm that the float connects to, is the only link to ground you should have on the sender.