Suzuki tend to call the shift rod the clutch rod, and it has a joint in it somewhere between where the lower unit bolts onto the leg and the undertray of the engine, dependant on what model you are looking at. As the instructions suggest, some are covered by a plastic housing.
On my 200V6 it’s just a couple of inches above the lower split.
If I was at home I’d scan a manual, but that will be later tonight.
I suggest you take a look at the microfiche type images on Browns point Suzukis web site, as they are better than a workshop manual.
Suzuki Outboard Parts Catalog Microfiche - Browns Point Marine Service
Should have said, I’ve made several copies of Suzuki special tools to get into the lower unit on my 200, I’m not sure they will fit your engine, but you’d be welcome to try.
Once inside it’s all pretty basic stuff as long as you don’t replace anything that will affect the shimmed length of the assembly.
Replacing items like the dog clutch, which might be your problem, doesn’t effect it for example.
I assume you’ve tried adjusting the shift rod etc already.