On most Olds valves, there's no way to directly apply oil to the back bearing. Olds got around this by putting an oil groove in the bearing and a passage between the groove and the bottom of the hole the sprindle screw goes into. To oil the bearing, you remove the screw and put oil into the hole.
EDIT: FYI, this core is from an S-20 Super bass trombone, s/n 3092xx. Based on published lists, it was most likely manufactured in the fourth quarter of 1959.