Connect both to complete the circuit...
I have had issues with my rear defroster as well, but here is what I know...
You will need both connections at the rear window to be connected in order for there to be any chance of it working.
The theory of a "lined" window defroster is that 12volts is applied at one side, and ground is connected to the other. The resistance of the lines themselves cause them to heat up when current flows between the 12volt source and ground. (When you push the button to turn it on)
Since the lines themselves are in effect a resistor, if you measured the voltage along the lines from the 12volt source to the ground, you would see the voltage drop as you moved closer to the ground connection.
My issue was that the lines were so deteriorated that they barely had continuity, and some had breaks in the traces. Any break in the line, and current will no longer flow through it - thus not heat up.
I only had about two lines working - none of them were where I actually looked through with my rear view mirror...
There may be a better way, and I welcome any suggestions from other forum folks, but I just bought about three of the liquid repair kits. I prepped the entire rear window defrost area using Prep-All grease and wax remover. I then used painters tape to tape off above and below each of the lines.
After that, it took almost two complete kits to get a good first coat on all the lines. I waited until the next morning and used the remaining kit to go over all the lines once more.
Let it cure 24 hours, and then I carefully took a razor blade and cut above and below each of the lines so not to pull up any of the repair material when I removed the painters tape...
I can't say that it works like new now, but it at least works to de-fog and defrost light frost and ice with 1-2 timer cycles of pushing the button.
Hope this helps...