Just took my first crack at it. My board doesn't quite match the diagram and has quite a bit of rework - cut traces, additional components, etc. I suspect it is from an early production run (date codes are all circa 1975).
I found the following:
Probed voltages in circuit and found that the +5V rail was at 0.81V while +6V rail was at 5.86V. Measured about 319 ohms from +5 to ground, so I suspected a bad diode. Took the board out and removed the diode (GR2401) and it tested good. Took out C2406 and C2308 and tested capacitance and leakage resistance, tested good. Put the diode and caps back in and re-installed delay board to do additional probing, and found +5V is now 4.92V and counter now turns on.
Tried to perform delay calibration per section 3.1 of lowimpedance's PM3261-c.pdf. Found that the count knob push-pull had dirty contacts, which was leaving it in "fast" mode and couldn't hit the count speed spec (item 7). Blew it out with compressed air and it now works much better. Now meets spec at 15.5 seconds / 10 count.
My guess as to how this is supposed to work is it just delays the display by N trigger events (N being from 0-9999 as displayed on the counter). This is similar to how the "Delay Time" knob works, but it's better because it's can scan through data(?) There's a press release describing it here:
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5183165.
However, I only get a trigger when the counter is 0 or 1. Outside this range the "NOT TRIG'D" light comes on and sweep stops if displaying the delayed timebase, or the trace highlight goes away if displaying main TB.
I think I need to understand Fig 3.5 of PM3261-c.pdf more fully before continuing.