The simplest answer seems to be that he didn't know that there was a secondary gunnery position because Rey didn't tell him that there was one. She advised him that the guns were down and that's where he went, following orders like a good little soldier.
At the point that he announced that his gun wasn't working properly, she then immediately lines up a shot that he can make, presumably rather than chancing that he'll be able to get to the other gun and start firing (assuming that they even work) before they get blown out of the sky by the TIE-figher.
Before the gun broke
She and BB-8 headed to the cockpit, where she ditched her staff and plopped down in the pilot’s seat. She flipped a switch on the console and the controls illuminated. A little dusty, perhaps, but perfectly readable.
“Gunner’s position is down below,” she called to the young man.
“You ever fly this thing?” he shouted back.
“Nobody’s flown this crate in years.” - Force Awakens: Junior Novel
and
“Gunner’s position is down below!” Turning, Finn headed for the
indicated area. “You ever fly this thing? Or anything like it?” - Force Awakens: Official Novelisation
After the gun broke
“Cannons are stuck in the forward position,” he said. “I can’t move ’em—so you gotta lose ’em!”
The young woman tried to shake their pursuer by diving into the center engine thruster of an Imperial Super Star Destroyer. All of a sudden they were speeding through a tight maze of shattered beams and crumpled walls. “Are we really doing this?” Finn asked in disbelief.
“Get ready!” she commed.
“Ready for what?”
The narrow confines hadn’t scared off the TIE. Its pilot tracked every move they made and pelted the freighter with lasers.
After a quick climb, they broke out of the destroyer into blue skies. Finn lurched in his harness when the young woman decelerated and cranked the freighter around to face their pursuer. The enemy fighter emerged from the destroyer, dead center in Finn’s crosshair. She had lined up his target for him. All he had to do was fire. Which he did. - Force Awakens: Junior Novel
The 'secondary turret' might be broken
Uninterrupted light appeared at the far end of the service corridor
down which she was flying. Another blast from the unrelenting TIE
fighter pilot nearly sent their craft crashing into the corridor’s
ceiling, and she only managed to correct at the last instant. There
was no time to check readouts to see if any critical part of the
stolen ship had been damaged. All that mattered was that they were
still airborne and the controls continued to respond to her touch. - Force Awakens: Official Novelisation
