I've just tried this with mine (after repairing it*), I couldn't get the lower speed board to work in the high speed position, even tried using a lower frequency external time reference, but it still doesn't work.
The 1962 manual (on BAMA) states the boards were originally 300kHz & 2MHz.
The lower frequency reference is something Advance did, but they swapped the crystal for one that allowed their counter to directly read in RPM.
*As received my 5233L powered up OK, but none of the functions were working.
First problem was the micro sized fuses on the back, the -15V one was blown, the +20V one had been bodged with a 5A? fusewire soldered across the pins.

For testing I've used some modern round 1A Wickmann type fuses, I bent the legs to hold them in place, the fuse caps do not fit. If I can't find the correct type I'll consider either changing the fuse holders to the suit the modern Wickmann type, or fit some alternate fuseholders inside. Look up GMW fuses on Mouser to see why I won't be buying them.

-group-therapy-thread/?action=dlattach;attach=2784289)
After this self check was still not working, I printed out the diagram for the sampling & gate control boards and the input boards. I also cleaned the contacts on the reset switch, as this type of switch getting dirty contacts is a common problem in old HP stuff.
I connected a scope up to pin 2 of the sampling control board (A26), I could get the signal to change when pressing the reset switch, also I noticed the counter appearing to work with the switch slightly pressed, just enough to open the first contact.
At this point I noticed this contact isn't shown on the circuit diagram (no idea why), but I also noticed some wiring that had got a bit melted and some poor soldering. Looking closer I found a white/violet wire broken off, this was soldered back to the same point as the other wire with the same colors.
-group-therapy-thread/?action=dlattach;attach=2784297)
Turning the counter the right way up to inspect the other side, I found more evidence of a failed repair attempt & melted insulation and for some unknown reason a white/red/blue wire soldered to the same contacts as two brown wires (there also was a whisker of wire appearing to touch the switch frame too), in the same area a broken off white/grey wire was found.

-group-therapy-thread/?action=dlattach;attach=2784301)
At this point I thought it was going to be impossible to figure out where there were supposed to be attached, as the early diagrams in the manual lack any wire numbering.
But thinking about it over tea, I had a look through the saved pictures of other 5233L counters and the picture on the previous page (thanks duckduck for the pic) and figured out where everything was meant to go.
Later I removed the brown wires, tidied them all up & reconnected the other two to the correct place.
-group-therapy-thread/?action=dlattach;attach=2784305)
On power up I now had a working counter, self check mode was good and the inputs were now accepting a signal, this counter is exceeding it's spec and counting signals over 4MHz.

One of the readout is quite dim, some digits light better than others, looking at the readout bulbs, most of them have a lot of silvery deposits on the sides on the glass, indicating this counter had a long service life.
-group-therapy-thread/?action=dlattach;attach=2784309)
-group-therapy-thread/?action=dlattach;attach=2784313)
A couple of extra pictures, one of the later 5232 board with the CMOS based display decoder and the A25 gate control board.
-group-therapy-thread/?action=dlattach;attach=2784321)
-group-therapy-thread/?action=dlattach;attach=2784317)
David