12.13v after sitting overnight? - you have a bad battery - if it were half decently healthy it would have been around 12.50 volts. I have 6 cars in the family to keep repairing and this test on batteries has never let me down in 7 years. If you still don't think it is the battery - try the test on a car that is working properly and compare readings. If you are still hesitant - borrow a battery from another car that is good and try the overnight voltage test and then try to start the car with the borrowed battery. I am willing to bet it will start right up. Load tests are great for final diagnoses - but is tied into the current draw of the battery - which the load test checks - however - there is a correlation with the voltage at the same time. So a battery that has a static voltage after 12 hours at rest of 12.56 or more - will most likely load test good. A battery that has a static voltage of 12.13 volts does not have enough reserve and will most likely load test bad. A real good battery will have a static voltage of 12.76 or higher. Here in Canada we have been using Crappy Tire batteries that usually last 2-3 years before going bad - but the low price and closeness of the stores keeps me going back. Every one of their batteries that I have static votage tested as bad - they told me that I was wrong and to prove their point - charged the defective battery and then left it to sit overnight - then load tested it - BAD. That is why I am so confident that the voltage test will work- experience.
Morris