Reverse gearing is either 3 or 6 cogs/slots, depending on the model of the engine. My 2002 was of the later design, had a triangular vs square mark on the top rear of the mid section. Reason was improved reliability with twice the mating surfaces. That comment and my following comments are based upon information in my service manual.....the parts about identifying 3 vs 6 mating points and the part about bending linkages. The rest of it reflects my experiences and comments based upon such.
Being vertical sided slots and cogs, the cog has to be right over a slot to fall into it when the shift lever pushes the "clutch dog" mounted on the prop shaft, to the rear. To engage properly, engine or the prop has to be turning when dog pressure is applied so that the components will line up and engage while there is minimal pressure on the shifting linkage.
If you have forced your shifter into reverse without the above you probably have bent a connecting rod and you currently can't push the dog far enough for a positive engagement.
What I would do if you asked me to fix it is first disconnect the shift linkage from the remote cables and with one hand on the shifter lever and the other on the prop, apply slight twisting action on the shifter while moving the prop until you find a high spot....aka the cog is not inserted in a slot. Mark that position of the shift lever. Return to your pattern and when you get alignment and the cog falls into a slot and the shifter moves all the way aft, mark that position.
Reconnect your shift cable and using your remote handle, and somebody turning the prop for you, go through N to full R and once locked in R, or once the mechanism has done all the engagement it's going to do, look at the position of the shift arm. If it's not as far back as it was in your initial test, your shift linkage (the barrel over the shift cable just inside the cowling) needs to be moved such that you can move the shift arm fully into R.
If you did significant running with this condition you may have rolled off the edges of the engagement surfaces and as a result replacement of the clutch dog and R gear will be required.
