Okay. If I were looking at this I would start in this area. The 5 supply ( 1.89 or 1.90 v ) is what feeds the channel display LEDs. Follow the 5 supply left to TR36. TR36'S base is fed by TR37.
Now.... follow TR36's collector supply down.... to R113 (68 ohm) and drop down to the rotary switch S402-1. Notice that is your mode switch (AM, USB and LSB).
It seems to me that is something is wonky down in the power supply in the area of the mode switch.. it might be able to pull down hard on the voltage feeding TR36.
if it pulls down a little (AM)... would cause your display to dim.
If it pulls down harder (SSB)... THAT would cause the display LED to blank out.
I would snoop around this area with a DMM while keying in AM or SSB.... and measure voltages around TR36.
If you key up and supply5 drops...
Look at the TR36 collector and base...
If the base does something funky... that could be turning off TR36 and dimming the display.
If the TR36 collector gets pulled down.... then something further down near the modes switch is pulling that voltage down and THAT is causing the dimming.
Good luck..... let me know.
Bob