I'm deliberately going over this again, rethinking the problem, looking for a trigger mechanism.
The shaft is a short, splined on both ends steel rod induction hardened. The little black thing was probably a protector for the exposed seal that rides on top of the LU casting where the shaft is inserted. The LU casting has 2 bosses with a clearance hole drilled to accept the shaft. No bearings are involved. You have the shaft seals, the outer shown in your pictures, one under that turned the opposite direction (seal oil in and seal water out), and the shaft. The shifting mechanism is a hardened steel "cam" with 3 detents (dimples) for FNR, which is inserted between these bosses and moved radially by the lower spline of the shift shaft. Each dimple is a different distance from the pivot point...the shaft. (Not moving, the shaft could be rusted to the cast alum. bosses for one possible answer).
The prop shaft is hollow on the front end and a pointed "cam" follower protrudes from the front with several parts behind it, including a spring which keeps pressure against the dimples in the "cam".....these parts are brass for the follower and an adapter with a hole in it, and the rest including the spring are stainless steel like the prop shaft...nothing much to rust here and this is low enough that low oil probably wouldn't be a big deal from a corrosion standpoint if the engine storage was vertical.
Part of the front end of the prop shaft outer diameter is splined and riding in this splined area is a sliding gear called a "clutch dog". This dog has sawtooth teeth on the front end and cogs on the rear. The parts in the previous paragraph are locked to this dog via a SS pin that goes through that hole I mentioned above, so that as the cam follower follows the dimples in the shifter cam, the dog moves back and forth along the prop shaft engaging the rear of the F gear, engaging neither, or engaging the front of the R gear. The gear is "gear grade hardened" as are the F and R gears and that process lends itself to little oxidation (corrosion) damage. The radial and thrust bearings are SS also....nothing much here to corrode.
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The fact that nothing move, not even slightly brings me back to the cast alum bosses into which the shift shaft is mounted.
The shift shaft is hardened steel and you aren't going to hurt it.
You are looking at the rear of one seal when you look down at the shaft. Directly below it should be another. Directly below that a cast alum boss which is part of the main LU casting.
Get a small drill, like a 1/16" and drill several holes in the seal to a depth of ?". Get a scribe or something sharp and using the holes gouge out the seal. Do likewise for the one under it if it has one...most have 2 seals.
With the seals out you are looking at the upper boss. Do you see any corrosion? Give it a squirt of a quality penetrating oil like PB Blaster and let it soak a bit. Grasp the spline with your vise grips and methodically attempt to rock the shaft back and forth. If you get movement, more PB and more twisting. Let me know when/if you get movement of any kind. Don't attempt to shift just yet.