So as I understand it my 2 flooded batteries are fully charged at 12.7 volts. So if my solar panel is providing 13-14 volts. My battery can’t store more that 12.7. So if I cut off the solar my battery would quickly go right back to 12.7 or so. Is this correct?
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Yes.
After switching off the solar, your battery would slowly drop to around 12.7V if fully charged. The higher voltage of the panels is needed to "push" more electrons into the battery. This is a simplistic explanation.
That's correct but it might not happen instantly. After charging there's a bit of a surface charge showing a higher voltage. Turning on a small load like a light for a few minutes will drop the voltage to the actual voltage. If it's 12.7 you're good to go.
When we're on shore power, the battery level shows 13.x. Haven't had much opportunity (or need) to rely on our single solar panel, and when we did, it was too shady to get much juice.