It could be the battery but probably not if its showing 12.6..... Remember the saying "keep it simple stupid"... Check an clean the battery cables at both ends. They carode both at the battery an at the starter an engine ground on all makes an models. There is a way to test this but just clean them. Then take the battery to a shop or parts store an have it checked. If it checks out good then pull the started. Its done usually with several extensions on a ratchet to reach around the starter. Then have it tested an replace if needed. Do not pull the battery cable while it is running. That was a normal test back when we used generators but really was not a good idea then. A large portion of the cars on the road today cant take this test an will cook the alternator trying to maintain voltage. You may not have a bad alternator before the test but after it you will. Test it by starting the car an checking the battery voltage. It should go up from 12.6 to 13.8 or more after starting, even with the lights on.
