An update on this: given I couldn't determine where the black wire was supposed to go, I decided to remove it altogether (I can always solder it back, if I eventually identify its purpose).
In terms of the overall repair, I started looking into the different circuit blocks, beginning with the square wave generator.
And it seems someone had previously played with pot R63, which controls the frequency of the wave generator.
I adjusted the frequency to be close to 205 Hz, as per the documentation, and the meter started showing signs of life.
On a quick check, most of the functions seem to work and are fairly accurate.
There is some odd behaviour here and there (e.g. with the + - AC slider set to +, if I set the rotary range selector to one of the k\$\Omega\$ ranges, the measuring needle goes all the way to the left; with the slider set to - or AC, it doesn't do that), but that may be just me being unfamiliar with this type of meter.