Most older motherboards used the Dallas real-time clock chip, which had
a cheapo oscillator built in, and could use an external crystal for
precision timekeeping. A good crystal will add a couple of dollars to
the price of the motherboard, but the clock ic itself was over ten
bucks. I use these chips in some other pieces of equipment and they are
very accurate when given a good crystal for a timebase.

I don't know what they put on modern motherboards. I throw computers
out when they stop working now.

However, the datasheet for the Dallas chip gives some hints that may be
useful here. If the chip is put in an electrically noisy device like a
computer, it can be accelerated by stray signals picked up by the clock
circuit. I believe that NTP machines (usually) set the RTC on shutdown,
as the cpu is more likely to be on time if it's been syncing itself
with an atomic standard.