Well, after pulling this from my repair queue again and going down a deeeeeeep rabbit hole I can give some useful information to people that have one of these that shows the "E 3" error message.
After replacing many dead IC in the unit, it powered up again but showed "E 3" in the display. My unit was acquired as a completely dead unit from EvilBay. What the auction didn't say: The previous (deceased) owner was a smoker. A heavy smoker. A very, very, heavy smoker. The unit was literally caked in nicotine when i got it. Absolutely gross. So I disassembled it completely down to the last tiny part and cleaned it in a solution of demineralized water and an industrial cleaner. Replaced several IC sockets that were corroded beyond repair.
According to the service manual, E3 means "counting chain error".
Now, the way this unit works is this: The internal 10MHz OXCO is internally multiplied by 10 to have an internal 100MHz time base.
The circuit is similar to what you find in vintage HP frequency counters: It uses a clever trick using a transformer (realized in traces on both sides of the PCB) that together with variable caps acts as an LC filter to grab and amplify the 5th harmonic of the 10MHz and then into another one that doubles that to 100MHz.
To make a long story short: The 100MHz was missing. You can probe it under the OCXO module on the PCB transformers under the OXCO. You'll need to connect the OXCO module through a (short!) cable for this. Standard 1/10th inch 2,54mm pitch.
In the end, it was the four trimmer caps in the circuit. They were FUBAR due to - you guessed it - nicotine getting in between the plates, changing their capacitance so that the filter was no longer picking up the right harmonic. It picked up the 30MHz harmonic instead of the 50Mhz and could not be adjusted further. The unit does an internal check of the multiplier on startup and just routes the 100MHz clock through the divider chain into the 8031 MCUs internal counter (the 8031 runs from the 10MHz clock). If it's not happy with the result - bingo, E3.
I now have a pristine working unit for my lab. Frequency counters aren't a thing anymore really. I like this unit because it has nice functions like counting ratios and especially useful: totals. Really nice to track if a watchdog triggers in a long-term test or counting any other arbitrary events. It's also super repairable - built entirely in THT technology using TTL, high speed differential MC10xxxx ECL logic and a linear power supply. I had no problems obtaining parts for it.
The only new units on the market seem to be:
Peaktech 2860 - 2,6GHz, 8-digtits - around €340 - not many functions.
Rohde & Schwarz/ Hameg 8123 - 2,6GHz, 10 digits - €2.400 - the successor to the 8122. Very expensive.
Here's the frequency multiplier circuit for the aficionados. Have a nice day!