FORTRAN 66 (108 98 Bytes)
FORTRAN 66, 108 98 bytes
PROGRAM D 2 WRITE (*,*) '4 8 15 16 23 42' CALL SLEEP(6420) GOTO 2 END It is certain that the computer in question had the FORTRAN compiler, as it dominated scientific and engineering fields in the era. I was born 18 years after the eponymous year, but during my math program in university we learned FORTRAN. One fun lecture we learned how to program on punching cards. It's not that easy to format it correctly here, there should be 6 blankspaces before each command and I could only find a reference to the Sleep-function for Fortran 77 but it should have existed already in Fortran IV and 66.
PS: We could scrap off one Byte by using label 1 instead of label 42.
PPS: If the computer in question uses punching-cards for program input you're all out of luck and the bytes don't matter anymore. :D .