OK... so went at it this afternoon on the lunch break... First... tried to find any thread on how to get to the lights so I did not have to find out as I went... found a couple of threads that mentioned taking the rear cover (Lights, License plate, into the rear side vents) out... Let's just say I decided that it was stupid and looked myself... sure enough... you can do it from the inside of the GTS... no need to take a rear cover off. I'll post the photos of what i did separately...
On the issue with the hazards... once I got the light out (plastic enclosure) I checked to see if there was any signs of odd things. Any signs of moisture, damage to the connector, etc. It looked good. When I pulled the bulb socket from the assembly, the bulb looked fine. Without touching the bulb I went and turned on the Hazards... guess what... it worked. Since I had gone through the trouble of pulling everything out, I went ahead and made sure the socket contacts were clean, bent them for a bit added contact pressure, changed the bulb anyway, etc. I put it all back together and we are good, at least a few hours later. I'll assume the socket was odd or the bulb was slightly loose.
As a precaution, I went ahead and changed all 10 3157s back there. 6 were in the brake lights, 2 turn signals, 2 backup/reverse lights. I figured I'd eliminate having to do it again and put in all new bulbs. I used Sylvania Silverstar 3157 bulbs. They are a little brighter than the originals. Let's see if this fixes the matter.
Given this... the fuse can't be the issue. The flasher relay may be flaky and intermittently failing... let's see. For now it works....
Ken, on the electrical system... I have no issues chasing it down... I'm an Elec. Engineer... with a schematic (have one in the service manuals I just picked up) and a meter... the lights cannot be that complex. Let's see what happens now. Hopefully I scared the components into working! LOL.