But, the "skinny" is that the mechanicals had specific requirements, which asssured accuracy and had to be no more than +/- 30 seconds per week! Most of the quartz watches and many of the modern mechanicals don't have a problem within that accuracy.
My one and only RR approved watch, is my Pulsar RR Approved watch,which has the Lumibrite dial. And, it's VERY accurate to about + 5-7 seconds PER MONTH! This watch had to be accepted by some railroad in the world, to be able to claim it's "RR Approved". My guess is, since the Pulsar is a Seiko cousin, that one of the Japenese railroads "approved" is for use by their personnel.
Here's a shot of the watch and one of the Lumibrite dial:
ENJOY your fantastic watch!
Cheers,
Ed