Weird noise after 4 speed install

I have heard that noise a few time; it sounds like excessive driveline backlash.
It could be anywhere between the clutch disc and the side gears or even loose wheels.
My guess is the cross-pin in the differential case.
or mismatch between U-joint caps and the retainers.
Here are some tests, all done with the engine off; do not skip down to the bottom, lol.
1) Put the trans in Fourth, attempt to turn the drive shaft. If your synchronizers have NOT been modified for "slick-shifting", there should be little to no movement.
2) put the trans in First gear, and same as above. In First, you are now going thru the cluster gear, introducing two more places of backlash, so you will be able to turn the driveshaft a tiny bit more.
If in either test you can move the drivshaft more than a couple of degrees, then you will have to check the slip-yoke fit and the Front U-joint. As for the U-joint there should be ZERO backlash in it. As for the yoke; almost Zero.
3) Set the parking brake. Then attempt to rotate the driveshaft again, at the rear end of it. There should be Zero backlash in the U-joint
At this point having NOT found any appreciable backlash, forward of the rear U-joint, the lash has to be inside the rear end
4) Release the Parkbrake, and put the trans in Fourth again,.
4A) If you have a working cone-type sure-grip; grab either rear wheel and see how far it rotates, and listen to the rear end. The SG locks the rear end parts all together. The remaining points of backlash are; a) the pinion to the crown, b) the side gears to the axle splines, and c) the cross-pin to the case, and d) the pinion gears.
Of these, the only ones to develop lash over the long haul are the pinion gears, which eventually start to cycle between the case and the worn side gears, AND, the cross-pin eventually "wallers" out the case saddles, especially on manual-transmission cars. These can all be fixed
4B) if you do NOT have a Suregrip then I can pretty much guarantee that the lash will be in the pinions or the cross-pin.
4C) if you have a Clutch-type Sure-Grip; this unit has four small pinions and two crosspins. I have not seen very many of those and never a worn-out one. They work by engine torque compressing the clutch packs via ramps on the pins and matching ramps in the case. With no engine torque applied, as in idling with the wheels in the air, they tend to be nearly as loose as are open diffs, so then I suppose they could sound like that, lol, altho I have never heard mine do that.
5) pinion backlash is supposed to be in the range of, .007 to .012 IIRC. There should be Zero lash vertically at the front pinion bearing; ZERO.
6) the wildcards;
An out-of-balance tire, or an out-of-round tire, or a tire with fluid inside of it, or a bent axle-shaft, or a bent wheel, or a bad driveshaft, or rusted-tight U-joints; can all shake the rear end quite a bit; But I have never encountered the shake also making a noise like this.
If you have tapered rear wheel bearings, they can clunk whenever you side-ways shake the rear of the car, or one time when you enter a turn, or switch back; but I have never heard axle end-play make that noise, and I run mine a lil loose on purpose.