Assuming that your DX has a manual transmission, the reverse light switch is
on the front side of the transmission near the top in front of the starter.
With the transmission in reverse, check for continuity between the yellow
and green/black wires coming from the switch.  If there's no continuity,
replace the switch and be sure to replace the seal washer.  Note that if you
connect the other pair of connectors together and turn the key on, the
back-up lights should be on.  Note that if you do wind up replacing the
switch, be sure to clean up the transmission case around it to help prevent
any crud from falling into the transmission.

Eric