Yes Driffield did come under the North Eastern Railway, and the survival of its records is perhaps not the best. However, in 1923 the mainline railways were grouped into "The big 4" mainline railways, and the Northeastern along with the Great Northern became part of the London Northeastern Railway (LNER) At this time there was no sick pay for wages grade, and on the merger the Great Northern Railway Friendly Society was opened for membership to all staff of the new amalgamated railway who would have been eligible had they worked for the GN. This meant that virtually all eligible staff joined the society. Its records survive and are held at Doncaster Borough Archive, King Edward Road, Balby Doncaster.So this is well worth a try to find records of your relative.
A 24 hour residential crossing was usually one where the gates were normally closed to road traffic, and only opened on demand by travellers,they were one step uip from an occupation or farm crossing where the owner of the land controlled the gaters as required. Instruments were provided at these crossings so that the approach of trains could be detected before the gagtes were used. They existed into the 1990s in the general area involved.