[G0HZU_JMR]

Ideally, I think a few more tests are needed first. I had a quick look at the circuit for this sig gen and my knowledge of valves is very limited.
However, I'm going to assume the valve that feeds the output is some sort of cathode follower and therefore it will have a reasonably low source impedance at the cathode.

I'm also going to assume that there are several volts DC here normally and a fairly large RF waveform in terms of Vpkpk. Maybe several volts pkpk? This is then tapped down via a 1k cathode resistor and a 1k pot // 500R. So I'm going to assume that the RF voltage at the top of the variable resistor is about a quarter of that at the cathode.

Also, any probe capacitance here is going to cause RC rolloff up at VHF because the RC timeconstant of those 1k resistors will be equivalent to several hundred ohms and maybe 20pF for a x10 scope probe and even more for a x1 probe. So probing here is going to give confusing/droopy results up at VHF even before you try fitting a buffer.

I suspect that the classic JFET+ BJT unity buffer (suggested by Karl) can be made to work here because it has low input capacitance. Much lower capacitance than a scope probe. I also suspect that the signal level at that 1k variable resistor is much higher than the spec in the manual for the sig gen. So you might not need any more than unity gain. Just don't probe the input of the buffer with a x1 or x10 scope probe or the probe capacitance will cause RC rolloff and much confusion. You also need a fairly fast PNP transistor in that unity buffer if you want to preserve the performance up at VHF.

Finally, I would suggest that once a suitable buffer is found (that works) that you share the DC power between the the buffer and the counter via the coax. This way you will only need one DC power feed to power both the buffer and the counter. The buffer has to live inside the sig gen, very close to the 1K variable resistor.