you're right to suspect the anti-roll bar drop links as these do 'rattle' when worn
I'd suggest getting the back of the car jacked up so the wheels are off the ground then grasp the end of the anti-roll bar fimly and give it a shake as there should be no slack in any of the joints
other possiblities are a worn shock abosrber top mount and a worn wheel bearing
to feel for these - jack the car up so the wheel is off the ground and shake the tyre from top to bottom and from side to side there should be no play in either direction. Any play in 1 direction will usually require a joint to be replaced, if there’s play in both directions then the wheel bearing may be at fault. If theres play only up and down its the strut top mount - to find this one you have to shake the suspension strut it self up and down with the wheel off the ground - so you may need to remove the wheel to check this one.
Now with the car jacked up on that side with the wheel about 2 inches off the ground use a steel bar under the wheel and lever the wheel up and down slightly, you should be able to look at the end of the axle and see if the suspension arm is moving up and down separately to the axle.If so replace the bush
To feel if there's a worn strut top bearing then lightly hold the spring by hand and have your assistant move the steering from left to right with the wheel on the ground - a worn bearing will feel 'notchy' through the spring. The wheel needs to be on the ground for the test to load up the bearing
or it could be the exhaust hitting the body