How long does it stay at 30+ amps? A minute or so shouldn't be a problem, but I would be worried if it stays up there much longer than that.
The basic check is easy enough. Pop the lid off the control box and stick a piece of paper between the cutout contacts. (If you tear a crescent shaped piece, it will stay in place easier.) Hook up a voltmeter between 'D' and 'E', then start the engine. At 50F ambient, you should see between 16.1 and 16.7 volts. The specified numbers go down by 0.1 volts for every 20F over 50F; or up for every 20F below 50F.
13.0 is on the low side if the engine was running when you checked; but would be normal for a battery that has just been fully charged and never had a load applied. If you apply any load at all, though, it should drop to 12.6 fairly quickly. (Again there is a temperature correction, but I don't recall what it is offhand.)