If his right eye is "stronger" then he will see the ball hit the bat. It will require his personal motivation and his coaches support to provide extra BP swing [right & left].
One year in the Goodwill Series in Australia, I selected 3 Shortstops and on the 1st day place one in CF and one at 3b. The player, age 17 from North Carolina was 3.8 [home to 1st] from right side. I asked him to try left handed, he said yes he always want to. I told him to concentrate on hitting to the left side of the diamond.
He hit .356 in 12 games and returned to HS in N-Carolina.
Wake Forest offered a scholarship and I advised the Coach to continue his "switch hitting"!
The Head Coach agreed.
He played 4 successful years with the cooperation of Coach.