The myth was that it was the time when Abraham Lincoln died, but it had something to do with being the best position of rest for the hands of early clocks. Some mechanical thing about avoiding some parts taking a set if left too long in other positions. Both could be myths as far as I know.
A more likely explanation is that the manufacturers logo centered at the 12 o'clock position is nicely framed in the V of the hands. Older clocks with the logo above the 6 are often set at 8:20 for the same reason.
In fact first time I heard of this it was about why Grand Father clocks were left set at 8:20 when not wound up.
Came across this 1976 ad for the Speedmaster Mark II.
Love it when price is included and a quick calculation for inflation equates to 836 GBP or 1190 USD in today's money.
Nice comparison to see what they were asking for the new LED quartz watches of the day.