You can try putting her on the center stand to get the rear wheel off the ground then put her in gear. Rock the rear wheel back & forth and try to listen & feel for slop at the u-joint. Not a "for sure" test & there is a normal amount of slop in the older drive lines so it can be deceiving. The only sure way is to pull it apart.
Parts are available from:
www.mgcycle.com they are good people.
You should pull it down before ordering because there are two different bearings & u-joints. Rear drum models use a different size than the rear disc brake models although some early disc brake units used the small set up. It's a time consuming job but really not to bad to do.
Be careful with the swing arm pivot bolts especially when re-assembling, they are a very fine thread and very easy to damage. The most difficult part is getting the swing arm to go back in and getting the u-joint to slip on the trans spline at the same time. Somewhere in this forum I read something about stuffing a rag under the joint to hold it up and then pulling the rag out so you might want to search for it or maybe somebody else will post with a trick. To get the support bearing out you will need a good set of snap ring pliers and a two jaw bearing puller like a slide hammer. You may want to just pull the swing arm off and carry it to a local garage or machine shop & let them swap it for you.
You may want to try this before pulling the swing arm.
It could be the ring & pinon has wear also. You may want to drain the rear oil & check for shavings. (Refill by measuring the correct amount which I believe is .360 litre or 12oz.)
While the unit is drained pull the rear wheel. There is a large circular plate with 8 bolts that can be removed and this will allow you to see if the surface of the ring & pinon gears are pitted or flaking. I am simplifying this operation as there are seals and gaskets that will need to be replaced & if memory serves there is a cage type bearing that may slip off. If a rebuild is needed then contact Charley at
www.zydecoracing.com
I don't want to offer advice that could cause you problems so don't attempt anything that you don't feel comfortable with. I have PDF parts manuals for the T & T3 series with exploded diagrams that I find extremely helpful to see how things go together. If you want copies shoot me a private message and I can email them to you.
Good luck and welcome to the forum.
Trout
PS: These old Guzzi's are worse than a heroin addiction.