Electronic – Timimg of 4060 counter-oscillator

You are probably correct about why you're always seeing a "1" on the display on power up. As C3 is charging, the Schmitt Trigger U2A will see it as a low voltage until the voltage on C3 exceeds U2A's minimum threshold. With such a large value for R1, it takes a long time to charge up C3. I'm assuming the pendulum is relatively slow if you're using such a low frequency low-pass filter.

An elegant way to prevent that erroneous behavior is to put a similar low-pass filter on the ~CLR pin of U4. If you choose an RC time constant this is slightly larger than \$R1*C3\$, it'll guarantee that U4 will come out of reset only after U2A has stabilized.

The ~RBI feature is actually easier than I think you are thinking it is. If you just hard-wire it to ground, the chip will automatically blank the display for zeros, but illuminate normally for anything besides zero. In other words, you can get rid of U9 completely and just tie the pin to ground. You can see from the datasheet that if ~RBI is driven low AND all of the inputs are low, the display will be blanked. If any of the inputs are not low (a non-zero number), it doesn't matter what ~RBI is, it will actively display the number.

Your basic idea looks good to me. There are a couple points to consider.

To get a precision of 0.5% in one run of your scheme, you would need to count at least 200 cycles, so you need at least an 8-bit counter. Looks like your 4024 counter only has 7 bits. However, that problem is easily overcome.

If you also need accuracy of 0.5%, you need to think about the accuracy of your 8 MHz crystal. (Here, precision means that your measurement is reproducible using the same setup. Accuracy means that your frequency measurement is tied to the SI second. Accuracy therefore guarantees that your measurement can be reproduced by anyone that builds a similar setup.) Basically, you are counting "ticks" of your unknown signal in terms of the "ticks" of the crystal oscillator. But what if you replace your crystal oscillator? The new one might have a different frequency. Then you would get a different answer, even if the frequency of the unknown signal didn't change.

I guess the frequency of a standard crystal oscillator is accurate to about 100 ppm = 0.1%, so you are probably OK. But check the datasheet for your crystal (again, for the accuracy spec, not precision or timing jitter).

Finally, you might worry about the precision of your crystal oscillator - exactly how periodic is the clock signal? But over these timescales I strongly suspect it will be fine at the 0.5% level. Again, you could check the datasheet.