I have read several entries on how to keep the MS8040 display lighting on while on mains power and even designed my own mod to accomplish that.
After having used it on mains power for approx. half a year (incidently), display brightness had decreased significantly.
Investigation shows that the design of the MS8040 display lighting circuit appears to overload the LEDs used, aging them rapidly resulting in reduced brightness (and unnecessary high drain from batteries when activated). Continuous use while on mains power significantly accellerates this aging because dissipation is increased.
I devised a fix for this problem.
See posting "Re:Part 2: Teardown/Evaluation Mastech MS8040 Bench DMM" my replies #17 dated March 20, 2020 and #18 dated January 16, 2021.