Probably a 90% chance it is the battery based on the age. But it could also be that it's not being charged properly. A 12.1V level is odd for a either a charged or damaged battery. Since each cell is 1/6th the voltage, I'd expect maybe 11.5V or less with a completely dead cell. However, I don't know what a degradation over time does in terms of voltage output.

Poor charging can come from several sources, obviously a bad alternator, but loose cable connections could do it, too, and that includes the three ground connections from alternator-engine-chassis-battery.

I knew of a case where someone drove just 2 miles each day and the amps to start it was more than the amps charging it while driving. That doesn't sound like it applies or isn't much of a road trip to my way of thinking.

12.1v is too low, at rest they would typically be up around 12.5 or 12.7 at rest so I would get a new battery