I also have the same two noises from my 1999 RX300 124K miles. The farting noise happened maybe 5 years ago and I have not been able to locate the source because it is intermittent. In my case, it usually happens when the Rx300 stops at signal lights with the transmission in drive or neutral.
It does not go away after changing transmission fluid. Two days ago, I have a major tune-up done (timing belt, idler, tensioner, all the belts, water pump, spark plugs, oil change, valve gaskets, cam seal, crank seal, 4 new brake pads, machine rotor, rotate tires). The farting sound stays. I just captured 3 occurrences of the sound after turning the video camera on while driving. This time it occurs around 26 min 31 secs and 27 min and 17 secs after starting the engine. I have to let the RX300 sit at idle with foot on brake pedal and shift at "drive" and wait. I did shift to different positions trying to find the condition that will generate the sound. When the sound occurs, it is only once or two times in a role.
I will upload the sound in my next reply to this post for comparison.
