I had a similar issue, that when I placed the turn signal switch in the left turn position, everything worked as designed.
However, when I placed the turn signal switch in the right turn position, the front lamps were correctly lit, but both rear lamps flashed together, as if they were in 4 way hazzard position.
I had pretty much narrowed it down to a bad turn signal switch, or bad fender mounted flasher unit.
Since it was easier for me to borrow a turn signal switch to test for bad parts, I swapped it out first and VIOLA! All my signal lamps operate as designed.
I found a good deal on a new turn signal switch on the E Place on Wednesday, and it was delivered on Saturday.
I installed it as soon as I got home from the Post Office, and it confirmed my earlier diagnosis.
HTH.
Jay