Same here. My older 89-IV started beeping in all ranges except current. Re-soldering the current jacks helped, but after a month it got worse, constantly beeping. I solder-wicked the old solder on the current jacks, re-soldered with basic rosin flux solder, and cleaned with flux remover. Now it works perfectly. But I was curious what the root cause for the problem was.
I couldn't find an 89 schematic, but I found an 85-87 schematic and assume the circuit is similar. On the 87, the lead sense circuit for the 10A jack uses a 10Meg pull-up resistor. The one for mA uses a 30M pull-up resistor. These are giant values and any board contamination could be seen as a logic 0, an installed lead. My meter had a previous battery leakage problem. That probably caused the board leakage, but dirt, oil, age, water, lack of board cleaning can also cause it.
Hope this helps.
Dave Erickson