Running lights
I would start at your headlight switch. I don't have a wiring diagram in front of me know, but obviously check the fuse first if you haven't already done so.
If you have 12V at the switch and it heads out when you actuate the switch you will have to start checking at the corners. I know on my 89 I didn't have any of the corner lights (Front fender sides). Replaced the bulbs but still no lights. Upon further investigating I found the leads in the plug for the bulb all corroded. Cleaned those up and put a bit of dielectric grease in there, been good to go since.
Don't forget some of those bulbs have 2 filaments, one could be junk (tail lights) while the other is okay (brake lights).
I would search on here, I know I found some wiring diagrams on here, those will be your map if you know how to follow them.
Worst case, keep posting. These guys on here are great and are full of experience and knowledge. There are multiple lifetimes of K5 knowledge on this site at any given time.
You might want to get your self a couple of long runs of wire to help troubleshoot. Put one on the negative post of the battery, you could use it to verify a good ground as you follow your 12v to each corner of the vehicle. One solid ground to the front, another to the rear possibly.
Being as your problem is all around, I would bet it is in the headlight switch or fuse for same. It's unlikely that you lost all of them at the same time unless the source is suspect.
Let us know what you find. I'm sure it will come up again.