Question, on the second round, are you sure the firing PIN is actually being hit by the hammer or are you seeing the normal firing pin peck on the primer that comes from a free floating firing pin during chambering? The fact that the first round fires and the second does not could be telling you that the bolt is not fully locked up, therefore, the hammer is not striking the firing pin at all and the mark you are seeing is just the normal peck the firing pin does when chambering.
If the bolt is not fully locked up, your hammer is not striking the firing pin at all. Not going into full lock up could be the result of things being tight and hand working the action a hundred or so times may smooth things out, or it could be the rifle is not lubed well enough. Make sure it is wet with lubricant during initial break in. Or it could be a gas problem.
When you fire the one round, do it with an empty mag in the rifle and does the bolt lock back? You could be slightly under gassed and the bolt is not traveling all the way to the rear, resulting in not enough forward momentum to fully chamber the second round, giving you the firing pin peck but not a hammer strike on the firing pin. Not enough gas could be caused by a misaligned gas block, the most common problem, leaking gas key or bad gas rings. Measure your gas block and gas port in the barrel to make sure the ports are aligned properly. Just ramming the gas block up against the barrel shoulder can partially obstruct the gas port in the barrel, restricting gas flow.
Are you shooting handloads or factory loads? If shooting handloads, you may not be setting back the shoulder enough and be creating short headspace. That allows a full drop the BCG to crush fit the case into the chamber and lock up fully but during firing there may not be enough forward force to crush the round in the chamber to lock up completely, especially if it is short stroking.