Pictures I looked at for Honda 90 4 stroke show shifter twisting not going up and down. (Not sure if model I looked at is same as yours). Go to Honda parts lookup: www.peparts.honda.com/marine#/serial
You will need model #, serial# and you can view a parts diagram for your engine. Another option is to go on iboats.com forum under engine repair section for Honda. There are several mechanics (mostly retired) that offer a wealth of knowledge. They encourage diagnosing your problem rather than throwing parts at it and will give advice on what to look for. Post your year, hp, model, and serial number with your question. For best help answer any questions they have for you.