Re: 1976 mercury 850 foot / lower unit
The shifting mechanism on Mercs works like this. Both F and R gears are driven directly from the drive shaft from the engine and spin continuously. On the prop shaft is a thing called a clutch dog that is moved along the prop shaft by the shifting cam which is moved by your remote control shifter.
For R, in the older engines, the dog has 3 cogs that fit into 3 square sockets located within the R gear and cause the gear to turn the prop.
Apparently this is a common problem as Merc increased the cogs and sockets from 3 to 6 somewhere in/after 1989. Since the gear is case hardened steel, I'd guess you could get away with just a new shift dog. If you are mechanically inclined you can fix it. I did on a restoration and it was my first time in the lower unit. Wasn't that bad, just pay attention to how you open it up and where things are.
Prop and washers come off. The big spanner nut that is threaded into the housing comes off. The shaft with rear carrier bearing and dog will come out as an assembly.
Remove the wire retainer from around the dog. There are 3 ball bearings preceding the spring inside the prop shaft where the dog is located so be prepared for them to fall out when you pull the pin and allow the shifter cam follower (front end of prop shaft) to pop out. Pulling the pin releases the dog and the spring. Slide it off, install the new dog and reinstall the other prop shaft parts removed, clean up your lower unit of metal shavings and old oil, and put her back together.
Your biggest challenge will be to get the spanner nut off as it and the threads are always corroded. Second will be pulling the whole assembly but putting the prop washers back on and using a sliding hammer you can bang the assembly out.
The big round oring on the bearing assy should be replaced and if you feel up to it, the prop shaft seal(s) too...might as well on an engine of that age. On some engines there are 2 seals back to back around the shaft. One with the lip pointed in and the other out so that you can seal against water outside and oil pressure that could develop inside.
WW has Quicksilver/Merc premium lower unit oil in the quart with the pump in the sporting goods section. When you get your parts, get a couple of new seals for the vent and drain screws....mine are blue. I understand they have a new yellow permanent type out now also.
With the engine vertical, pump oil into the drain plug till it comes out the vent hole (right side of engine just above the antivent plate...has a stainless steel screw sealing it, just like the drain screw) and allow a little to continue flowing reducing the bubbles. Insert the vent screw AND NEW SEAL and tighten. Remove the filler adapter and install the drain screw and NEW SEAL. A little fluid loss is normal but try to keep it to a minimum.
Testing: F prop hard to turn CCW, clicks CW, N prop disconnected, R..WHILE SOMEONE IS ROTATING THE PROP ALLOWING THE COGS TO LINE UP, shift to R and in R the prop has resistance in both directions. If all that works, you should be good to go.
HTH,
Mark