Morning Roscoe,

I have GONE OVER your "FLASHING" elements...
Even the headlights are sourced to a different ground (G112, G113)... which would indicate something even MORE basic.
Unless your transmission is MANUAL
(There's a specific TSB on wire-harness being chaffed by clutch operation)

Your description of "FLASHING" items ... versus everything working until you turn "on the head-lights..."
Leads me to suspect the ENTIRE body ground (which I have NOT BEEN able to locate on these... bbbind.com drawings).

I have found references to a "Body-Frame" ground
(G305) on your left front fender... but have been unable to
Isolate any specific reference to your FIREWALL - ENGINE "strap"

Rather than initiate a a GRAND HUNT... for any missing straps..

This rather BASIC hypothesis could be easily DISPROVED simply
By measuring the HEADLIGHT voltage... against your BATTERY's GROUND...!!

If the voltage (B+) is present... it is your BODY GROUND
(Not FRAME & Not Engine Ground)...

Hope that helps!
Repair Guides Connector Ground Locations 2002 Connector Ground Locations...

What is everything blinking ? headlamps , dash lamps ,what else ? The headlamp switch is an input to the central timer module !
Also does it do it with headlamps hi or low beam ? Don't know what relay you replaced , there is no headlamp relay ! There is a park lamp relay ! http://bbbind.com/free_tsb.html Go here an check out wiring diagrams . Enter your vehicle info. Then under system click on lighting ,then under subsystem click on exterior lighting !