It should be really stable! I'm betting we are talking about a 20ns jitter over a 1 second period.
I really like the idea of using a known clock to time the jitter, although I'm not totally sure if the clock can be trusted.
A ramp and hold could do the trick! But again, we are looking at Parts Per Billion accuracy. I would have to go for a 8 digit multimeter or higher precision!
The ramp and hold is done on a fractional remainder signal, (eg 1us in 1sec) not the whole time base, so nothing special is needed.
This sounds very similar to a GPSDO problem, where they have to filter a 20ns jitter from the GPS 48MHz oscillator, and use it to long term lock a OCXO.
Here, you want to measure the jitter. If it is stable enough, you could lock a OCXO the same way, and then focus on the 20ns jitters via a better TIC.
There is good info here
https://www.eevblog.com/forum/projects/lars-diy-gpsdo-with-arduino-and-1ns-resolution-tic/The TIC here is only good enough to lock, so it is not calibrated nor very linear.
If your problem is the same, of known size clock qanta/jumps,. you do not care so much about getting that to 1ns precision, you are more interested in 'how many and how often'.
Is the clock jitter in an MCU cumulative? If so, even a really high quality clock would not be able to measure the 20 ppb (ish) I'm looking for...
A MCU with a good enough external clock will be fine. The PLL does not have accumulative jitter.
Even a Pi PICO might be useful, doing a dual capture of your signal, and a GPS 1pps, or better, a GPSDO 1pps.
google finds a useful plot of their typical crystal
https://forums.raspberrypi.com/viewtopic.php?t=309414#p1851013Maybe someone makes a Pi PICO module with a TCXO ?
Addit: I did find they recently improved Pico SDK to support more FREF frequency choices, in Feb2023, expanding the std 12MHz Xtal.
You still need to achieve a 125MHz and 48MHz USB clocks, from a 750~1600MHz VCO, but a 10MHz OCXO drive looks like a small step.
This thread modifies a std PICO board for external FREF, and reports the results
https://www.eevblog.com/forum/projects/pico-frequency-counter-using-rp2040/