Tee into the black line going to the transmission modulator and go for a drive. At idle and not moving, you should have somewhere around 12-15" of vacuum going to the modulator. Under strong acceleration it should drop to ~5" and at WOT it should drop to 0". If you have good vacuum going to the modulator, there's not a lot you can do but live with it. Rebuilding a differential is not for the faint of heart, it would be a lot easier to source a replacement or have yours rebuilt professionally, especially if the gears are worn.

__________________
Current stable:
1995 E320 149K (Nancy)
1983 500SL 120K (SLoL)

Black Sheep:
1985 524TD 167K (TotalDumpster™)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)