Those beeping sounds are in the mono mix, but were never used in any of the others until the special edition came along.
It’s also worth noting that the beeps are mixed at a relatively low volume in the mono version, but are much louder in the SE, which is completely typical of all the audio changes made to the soundtracks from 1997 on (everything is loud and in your face rather than leaving any room for subtlety).
Really? Were they not even present in any pre-Special Edition VHS releases?
None of the pre-1997 video releases used the mono mix.
Some content from the mono mix was mixed into the 85 and 93 audio. For example, Threepio’s tractor beam lines and such. But apparently they didn’t do the targeting computer noises until 97.