Agree with Bike DR, leave the small wires off and see what does not work (that's what I do). They could be your parasitic current drain and reason for the battery running down . . . Maybe something the previous owner installed, CB radio, etc. . .
Your battery should read around 12.7VDC fully charged. More likely it will be a little less than this, but much lower than around 12.2V is an issue. Once you start the engine, voltage across your chassis battery should rise. Depending on state of charge, the alternator will put out all the way up above 14VDC to charge your battery. If you get the rise, the alternator is basically working (you could still have regulator issues, etc..., but chance is small).
Do you have and know how to use the Amp meter function on your multimeter? This is useful for checking for parasitic current draw (that your two small wires might be placing on the battery for example).
Hope my ramblings help a little . . .
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