i just went through the same thing yesterday...wierd :nuts:
my front blinker was just broke and it was the plug itself
as of your lights going on at the same time, just do what i finally ended up doing yesterday.....
take off both rear lights....
unhook the trailer plug till later
make sure there are no crazy splices anywhere..if there are, fix them
chech all the wires for corrosion or breaks
wire everything back how it was supposed to be.from stock..theres schematics here on this forum if u need them
get everything working good, then put in your trailer lights...
the reason your stuffs dim is cuz your stealing power from it somewhere, and thats a no no
ya, headlight plug..your prob right..just put a new one in for a piece of mind if anything..i replaced mine yesterday too.
the reverse lights should not be connected to the blinkers
you need to get in there and replace and fix
good luck!
hope i at least helped a little :thumbsup: