The 1964.5 and 1965 Mustangs had unique "Mechanics" style internal clip u-joints which are not as common as the external clip 1310 U-Joint which was used starting in 1966. My 66 is a piecemeal of 65 and 66 parts used for a V8 swamp. My driveshaft and 8" both came out of 1965 cars, the rear end has a casting date of August 1964 and Driveshaft came out of 65 also.. it was pulled from a 65 with a 25 spline 3 speed and mated up to my my HEH-P 25 spline Toploader... the u-joints were expensive when I purchased them, I recall them being made by Spicer.

 

The u-joint should be snug between the "bumps" with no visible movement along your green axis.
The caps come in 1" and 1.0625" diameters. A 1" cap will be loose in a 1.0625" yoke.

 

The ujoint only moves side to side in a parallel motion to the green line, nothing perpendicular to the green line. I'm thinking DM289 might have nailed it because the original ujoint was too short on the yoke side (along my green line) it may of had clips but I can't remember. I'm the one that thought it was too short and went with a different ujoint. It was probably correct all along I just wasn't aware how the early style worked.

 

The u-joints are located by the ears on the pinion yoke, not the clips. Clips are strictly to retain the caps in the driveshaft and trans yoke, whether inside or outside snap ring style.

All 65-up 8" rears used the same pinion yoke, C3OZ-A, which appears to be used throughout the 70's as well. I'd clean your yoke up well and measure the diameter of the seat for the caps, and the spread on the ears to verify it's not damaged.

If a new u-joint that fits correctly does not solve the vibration, I'd look into the rear axle itself. I chased a vibration in my car for a while, which turned out to be failing pinion bearings. You should be able to hear that with a mechanics stethoscope on the pinion support.

 

I may be missing something, but the rearend in your picture is a 9 3/8" not a 8".

 

That's just some random internet picture. Car definitely has an 8". I've replaced all the seals on it in the last year and all the seals were the original ford's with felt instead of rubber. I believe the yoke and driveshaft are original.

 

A photo of your actual differential may reveal something that's been over looked.

 

Oh it's easy to see the problem. At some point someone put a 9" axle in your car. You don't have a 8". I'm going to say the 9" yoke on there needs a 1330 U joint which is bigger. Your driveshaft uses a 1310 U joint, you need a 1310/1330 combination U joint. Pretty common any good parts store will have it in stock.

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These are u-joints on my stock 65 San Jose 289/c4/8” axle.

The rear has 2 different size caps.
Hope this can help.

 

In your first post, you said the shop straightened the driveshaft and balanced it, right? If so, have you tested the car to see if you still have the vibration after this work? Before "fixing" anything else, verify the vibration still exists if you haven't already done so.

 

No I haven't tested it because when I slipped the ujoint into the yoke there is a decent amount of play maybe a 1/16" along the green line axis. I wanted to address this before moving on, plus right now there is snow on the ground so it maybe a while before I can test again.