A normal lead/acid cell that's fully charged will have a voltage of 2.1, for a total 6-cell voltage of 12.5-12.6 but using the electrolyte as a test medium isn't a very good method. With a sealed-top battery that's about the only option, but it isn't very effective. It's beginning to sound like the battery is a good part of your problem, but that oddball charging voltage reading needs to be corrected. Here's another quick load test- - - -disable the ignition so the engine won't start, and crank the starter for 15 seconds with a voltmeter attached to the battery posts. After 15 seconds, with the engine still cranking, a good battery will be above 9.5 volts. Don't run the starter much longer than 15 seconds or it can overheat and damage itself- - - -definitely not more than 30 seconds.
Jerry
