After more investigation today I think I've now found the true root cause of the problem:-
The counter contains an AGC loop.
This uses a diode detector which feeds a 741 summing amp.
The 741 adds in a variable dc offset voltage to set the gain using a trimmer.
I assume the output from the op amp eventually goes to the second gate of the dual gate MOSFET in the front end to control the gain (although I've not checked that).
The detector uses a pair of diodes in a voltage doubler configuration.
When I tried to measure the voltage at the detector output I got zero even with a 1V rms input connected!
At first I thought the problem might be the electrolytic capacitors in the detector. When I checked, the values and ESR looked ok.
Then I checked the two diodes using a trusty old analogue multimeter.
It turns out that one of the diodes was open circuit.
This is the first time in all my years as an engineer I have ever come across a failed signal diode.
The diode has no markings and I don't have a service manual, so I can't tell what type it is.
The older TF2430 used a single MBD102 schottky diode as the detector.
I assume the TF2431 also uses schottky diodes.
I don't have any MBD102 so I substituted an FH1100.
Low and behold - The counter now works as it should!
The detector fault explains the 120MHz oscillation I was seeing: The front end amplifier was operating at maximum gain all the time, even when a signal was connected. The oscillation only happened when a cable was connected to the input.
It's been a tough nut to crack and taken 3/4 days to trace and fix the fault.
It would have been so much easier with a schematic.