The testing that you are describing is what is called a parasitic current drain test. If you were to touch your test light between the battery negative terminal and the negative battery cable, with the cable disconnected, and your test light lit, then it means there is something drawing current. If this test revealed a test light that is on, with the key off and out of the ignition, doors closed and in no way there should be anything on, then you have a drain on the battery. The problem with this test method, is that you don't really know how much current is being drawn. A general rule of thumb is no more than 50 milliamps. Do you know what the brightness of your test light will be at 50 milliamps, 100 milliamps, or 5 amps? It's impossible to tell. With a vehicle of this year, I'd bet the current drain should be less than probably 10 milliamps, or in that neighborhood. If you have no trouble starting the vehicle in the morning, or after its been sitting for a day or two, it is unlikely anything is drawing current when it shouldn't be. You would have a dead battery if there was, which would result in a slow crank or no crank condition.
I would test your battery first. If the battery has a few years on it especially. It sounds more like the alternator is being overworked, if you have a dead or shorted cell in the battery, it can cause the conditions that you are experiencing.