this was a problem because a multimeter such old, review to label of manufacturing date, it was about 1996.
ok, search Google, to find the service manual of a model stopped production at long time ago, it will be something like treasure hunting, this time is lucky, the service manual and schematic has been there found.
In case you want more other model of Fluke product and service manual, I will recommend to search the website owned by Fluke, this 77 II service manual can be found also,
According to the service manual, beeper (just a raw piece of piezoelectric disk) has nothing to loose but just connected to GND and the BPR1 (pin3) of IC chip U1, the analog processor, so, if IC has malfunction, then the game is over…..or modification ?!
Try, clean the beeper rubber contacts and PCB solder contacts……
yes, it recovered almost loudly as usual, and looks like problem had resolved.