Side lights not working on 78 corvette

did you check the light switch? or a broken wire

you need new headlight

You will need to rebuild the headlight motors. You can buy the headlight motor rebuild kits with full instructions from ZIPS.com or any of the online Corvette restoration parts suppliers.

Your dash light...(instrument panel fuse is blown) or the headlight switch is bad...If you need any parts...the internet for corvettes is awesome. Hope this helps...(Just over 100,000 ) corvettes were made in 1975...

Check to make sure your door jamb switches are ok.

EATHER YOU HAVE A BAD GROUND OR A BAD HEADLIGHT SWITCH

Raise the headlights, either with the switch or manually by turning the knob on the headlight motor counter-clockwise.
Unplug the lights NOW to avoid an accidental closing on your fingers,
Remove the 3 philips screws holding the black plastic surrounding the headlights, and slide it forward, there is a small clip on the top that helps hold it to a corresponding clip at the top of the headlight,
Look inside the cavity and you can see the 5 nuts/bolts ( 6 on later years ) that need to be removed,
If you are on the driver's side you can now remove the whole assembly, on the passenger's side you must first unplug the headlight door control module.

I don't know about your 'vette specifically, but many cars use vacuum actuators to control where which vents receive the blower's air. This symptom suggests you have a broken or disconnected vacuum hose.

Maybe a relay but maybe and more probably a broken wire Get a diagram Chilton or Haynes manual

All the diagrams for your corvette can be found here:

http://www.autozone.com/shopping/repairGuide.htm?pageId=0900c1528008370b

Headlight wiring is towards the bottom of the page.

Hope this helps, have fun wrenching on that vette.