Brake Release or U Joint issue - "pop" or "kunk" noise when releasing brake pedal

Toyota 4Runner 2000 SR5 (RWD):
I’ve been noticing that when I come to a complete stop, then release my brake pedal, there is a pop or a “kunk” sound in the rear of the vehicle. The noise can also be felt. It happens before any forward/reverse motion can be engaged. The frequency is about 30-40% of the time when I brake and has been going on for about a year. The issue is not effected by time of day or temperature outside, however, if I am only driving 5-10 mph then brake, the noise much less likely to occur if at all.
I’ve taken the car to the dealership twice with no fix to the issue. The first time they sanded down rust on the rear brake drums (I believe) and this time I asked them to check the U-joint and brake calipers as well. I took the repairman for a test drive and I was able to show him the sound/feel that I am complaining about. Maybe it needed more grease on the joint. Or the brake caliper had too much “play.” In either case, today they told me it is working as it should. I still believe it is abnormal. Please comment on my issue.

The rear brakes may be twisting the rear axle forward and releasing the brakes releases the tension in the suspension. If you watch the rear axle while someone holds the brakes and guns the engine momentarily, then immediately releases the brake you may see what is happening.

Automatic or manual?

If it’s an automatic, I’d suggest that the engine may be idling a bit high (IAC problem) and loading the driveshaft, resulting in the situation that Rod describes.

In either case, you may want to check the sway bar bushings. The bushings that hold the bar to the frame can wear, as the bar turns in the hole, and if the holes get too big a thunk such as you describe can result. Usually it’ll thunk going over bumps too, but it’s free and easy to check.

Beyond that you’ve got drag links, coil springs, sway bar links, and other things that might store energy. Back it up onto ramps, and with the engine off, parking brakes on, front wheels chocked, etc., slide underneath and start shaking anything under there that looks like it might store energy. You can’t hurt anything, and you might get lucky.