Macbook Pro (mid-2012) detects adapter/battery but will not charge
After borrowing several different power adapters, I determined there was something inconsistent. The mid-2012 MBPs come with the MagSafe 1 "L" connector power adapter, but the pin layout is the same as the "T" connector models. I tried two of each and the L hasn't been able to charge my battery and the T charges consistently. Each time I made sure to use the right wattage adapter, which is 60W for this model.

I can't explain this, but it's charging now. Leaving this in case anyone else manages to dump water on their Macbook or have it fail in a similar fashion. I'd love to know why it works with only T connector adapters, but I'm guessing this is such a niche question it has not been looked into. I have also determined that in the "Power" section of System Report, it gives full power adapter info (serial number, model, etc.) for the T connector adapters I have used but not for the L connector adapters, so it seems to be an issue with the charge control (middle) pin on the MagSafe.

Long story short, always try another adapter if you have any others available. Switching to a different connector type fixed my issue.