If the meter is the same as the one on Amazon (the diagram you posted is identical) then apparently it's intended for one way drain and not charging. Note that the diagram shows the use of a 12V power supply and not a battery.
If you want cheap use a digital voltmeter which can help. Maybe even free at HF. Tables will give you the state of charge (SOC) for the battery voltage when rested. Observe and learn and how the battery is discharged for various loads. If it's 12.1V at 2:00 AM it's already 50% discharged and will be dead in the morning for example.
I use the Trimetric battery monitor and I'll let others suggest ones with less cost.
Is your battery a Marine deep cycle type? If so it's not much better that a starting battery and certainly NOT a deep cycle battery. Furnace fans consume a lot of power and you may need more/better batteries in order to use the furnace.
