That chip is a counter. It counts 'time'. This time comes from pen 3 of a NAND port in IC203. I don't have the name of IC203 but I think it is a common 4093.
The count is interrupted at the moment that it represents the measurement, I think this comes from pen 4 of IC203. It resets and the cycle is restarted.
With a means to visualise these 2 signals (scope, frequency counter) you might want to experiment and build some emulator that can replace the HCT6010A. How far you want to go will depend on the (sentimental) value this BKP 820 has for you.
btw: Are you're certain that the HCT6010A is dead and not something else?