I'm not familiar with that particular board (or many real arcade boards).
Are you saying there are four for each steering wheel?
Not sure if I'm telling you stuff you already know, but usually there are 2 sensors.
Each one consists of an emitter and receiver (a IR light and a light detector)
When the slotted disc is turned, it alternates between letting light pass and not, so you get a pulse.
The sensors are spaced so that the direction can be determined by how the pulses are timed.
The pulse from one sensor is labeled A and the other is labeled B.
The output would look like...
A_BOTH_B_NEITHER_A_BOTH_B_NEITHER_ for one direction
A_NEITHER_B_BOTH_A_NEITHER_B_BOTH_ for the reverse direction
So it doesn't make a lot of sense that one direction would work and not the other, at least not on the usual setup.
Looking at pictures online this game has another sensor that is blocked when centered.
Maybe the game looks for that one to be tripped before allowing the car to turn the other way?
Also if there are two extra sensors that are tripped when the wheel is all the way in either direction, I'd look at the left one.
If the game thinks you're already turned all the way left, it's not going to let you turn left.