Yes, it is possible that worn teeth on the steering clutch discs and hub will allow movement in reverse but not forward.

Just wanted to say thank you for all the replies here. My father saw the issue more than I did. From his explanation the right track would pull fine for about 2 feet then slip and jerk a few times then start pulling again. Cold weather and rain have prevented any work so far, but our first step as soon as it dries up a bit is to drain the right final drive and put a bore scope in there to have a look around, as well as checking the oil that we drain for metal shavings or pieces.

The seller has the books but its about a 80 mile trip one way to pick them up. In the mean time I have purchased the service book off of ebay to help us along the way. Once we know what parts we are needing the seller has offered us one of 3 parts machines, complete minus the engine.

I don't know how to rate the under carriage except to say that the track is not slipping on the sprocket. There is some wear but nothing I would suspect that would cause
an issue over the next few years at least, as this will be used on a farm.

Once we get started I will post some photos, not sure if I can do that without being a paid member, but you folks have been a huge help already so I'd be willing to pay to post
photos if I need to.

As for the bevel gear shaft, I would think if it had enough play that would cause both tracks to stop pulling, but you could drive in a straight line and never have an issue until you release the left steering clutch and wanted the right track to pull on its own.

You all have much more experience with these machines than I, please don't take any of my comments as argumentative in the least.

For one thing the tracks are way to tight. The sprocket does not look right either, it looks to far forward in relation to the dirt guard. Could be the bearings are gone on the sprocket hub thus teeth broke off on the gears. Hope not.$$$$$

The seller did tell you that the tractor had a final drive problem, so you can take him for his word, you have a F***** final drive that needs tearing down, my guess you will need to remove the right steering clutch as well to replace the pinion. Parts will include a pinion, bull gear, bearings and seals at minimum, maybe a sprocket hub and even a dead axle, if housings are worn badly even them as well. If it hasn't been run much after failure damage hopefully has been kept to a minimum, if it has been driven much then the damage will be greater.

Hopefully the donor machine has good componentry so that you will only need bearings and seals and a Caterpillar press. Make sure the donor is an 8U and not a 9U as some components will not exchange due to tthe different track gauge.

Wombat

I agree that the RH final is messed up. The sprocket is way too far forward. That means you have bearing issues with the sprocket drive shaft at a minimum. Time to start tearing down with some specialized pullers.

A pry bar to the sprocket to see if it is loose will tell you.But loosen the tracks a little first

Test 
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We were able to get a look inside the final drive today. The big gear is rounded in the forward direction of travel, in the reverse direction it is still in good shape. I suspect that when it started slipping a previous owner tightened the track in an effort to prevent slipping. I believe the angle of the photo I provided is only making the sprocket appear out of position. With the track open and laid out and the back of the tractor raised to clear the track there is no play in the position of the sprocket. It is also centered with the outside bearing carrier. I also took a better photo straight on of the sprocket.

you can see that sprocket has done some work and is a bit worn. one of the chapters reproduces a set of the cat track measuring guages that takes all the important track wear measurements. track sprockets can be rebuilt with replacement rims. another member even replace his without dismantling the assembly. as you have worn final drive parts it would be worthwhile taking the sprocket off and replacing the worn rim while you have it apart.