Running lights are on a different circuit than stop and signal. It sounds like to me that previous owner may have taken a signal off the front running lights to tie into the rear running lights, then since you corrected all the botchery they don’t work again. I say this as you said the under hood was a mess with 5 relays etc….
Have you ever checked or replaced the headlight switch itself?
This will be easier than you thought to find and you WILL get it! I am assuming you have a proper wiring diagram for the year/model you are working on? If not, get one. Then it is simply a matter of tracing back and following every wire to make sure it’s correct. It will probably be something simple…