The on/off switch opens the battery pack (-) to GND, which might be confusing.
The multimeter IC has a 6.5V regulator which powers everything except the Ohms source gets raw 9V.
I haven't seen a Beckman service manual on the web, I used to have a paper one but would have to dig for it.
The TECH 350/TECH 360 Owner's Manual has a tiny partial schematic.
Battery lifetime is rated 12,000hrs so adding an LED seems unusual.