If one battery is 12.34V whether the grader is running or not, it sounds like it's not being charged or discharged. i.e. it's not connected. The other battery at 15.54V is being horribly overcharged. The alternator output of 27.2V seems too low to charge two batteries in series. I'd expect something over 28V. Even adding the two battery voltages together gives 27.88 rather than 27.2 so none of your measurements match up with each other.
I don't know your history with this machine, but if it's new to you don't assume that the previous guy knew what he was doing. Go back to the beginning and trace every wire and connection. Check them all for tightness and corrosion. Check the voltage drop across each cable in case one is going bad. Ask all the dumb questions that are so obvious that they don't need to be asked. I'm talking about things as dumb as "Did I plug in the power cord?". Yes, I realize that doesn't apply here, but you get the idea.
Ed