I would strongly suggest that you get someone with experience in troubleshooting Raymond forklifts, and pay them. I think your local Raymond dealer, most likely, will provide you a wire diagram, (most likely for no fee) but without considerable training in how modern motive battery forklifts, and Raymonds in particular, work, it will not be much help. you are far more likely to spend more money trying to decide what part you want to replace, than the service call and labor time to troubleshoot will cost. There are concerns that electric traction controls have, that do not exist in other electric applications, such as "flyback' and 'plugging' currents.
all that said, if you have forward [forks first] acting correctly, then your problem is either in the control circuits that provide power to the contactors, or the contactors themselves.
Does the click you hear just before you start to move forward also happen when you try to go into reverse? does the 'end of driving' click happen the same in both directions?