two potential issues -
1. The throttle cable should just increase and decrease the fuel flow by adjusting the fuel rack for the high pressure fuel pump assembly. When it is set to low fuel position (e.g. neutral and both minimum throttle in forward and reverse) the idle adjustment at the engine should be against the idle adjust set screw. Set the idle speed using the positive stop screw on the high pressure fuel pump assembly (look in the Yanmar manual for specs but about 850 RPM).
2. If the cable is not getting pulled in the reverse position, it is probably the throttle lever assembly at fault and it should be checked. The throttle lever assembly is set to pull the cable in both forward and reverse. It also could be a corroded cable that is sticking, preventing it being pushed in for idle speed.
ps - Yanmar service manuals are posted on the
J/30 website at this page.