1963 40hp. The free play in gear is normal due to the design of the gears and shift clutch.
The prop should not "ratchet" in either direction when in forward (or reverse) gear. It should come to a stop either way.
I'd expect that you'll find the "ears" on the clutch dog, and the corresponding groove in the face of the forward gear, are damaged/rounded-off and this is causing the L/U to jump-out of forward gear.
Both shift clutch and forward gear will likely have to be replaced, since once the L/U starts jumping out-of-gear they become damaged beyond repair very quickly.
And if one bad part is replaced without the other, the new part will quickly become damaged and it'll just start jumping out-of-gear again.
Also check the aluminum shift clutch cradle for wear, in extreme cases there will be deep wear grooves in the side of the cradle. Renew as necessary.
Be sure to check the shift linkage for slop. It's very common for the clevis on the upper shift rod (which attaches the shift rod to the shift handle shaft) to loosen, then there's a lot of lost motion in the shift mechanism, leading to gear-jumping. Unfortunately, if the clevis is loose/sloppy, you'd have to pull the powerhead to gain access for repairs.
There is also an adjustment to the shift handle, when you're done you need to make sure that when in forward gear, there is a slight preload to the Fwd side, ensuring that the shift clutch is positively engaging forward gear.
You can tell when you've got this right by feeling a bit of "scrubbing" when in forward and turning the propshaft to and fro. The scrubbing you feel is from the ears of the shift clutch rubbing on the face of the forward gear. The slightest pressure on the shift lever to the neutral direction should stop the scrubbing.
With this adjustment, it should shift cleanly into neutral, while still engaging reverse gear as soon as you move the shifter in the reverse direction.
There are many years of 40hp engines, up to 1986 or so, to source parts from. So maybe you could find a good used later-model L/U on Craigslist for cheap. Later motors had a better design on the shift clutch (spring-loaded) and this gave a better shift action while being less prone to jumping out-of-gear.
To use the spring-loaded shift clutch feature, you'd also have to have the spring, balls, and propshaft with a hole drilled in it for the spring (basically the matched set).
At any rate, that's the lowdown! Pretty easy to work on once you figure out how to get into it. A manual impact tool works great for busting-loose the gearcase halves screws. Reseal with Permatex No. 3 on the gearcase flanges and also on the screw threads.
Here's a parts breakdown, FYI:
www.marineengine.com/parts/johnson-evinrude-parts.php?year=1963&hp=40&model=RD-25&manufacturer=Johnson§ion=Gearcase+Group
HTH & G'luck with the repairs.......ed