The rear turn signals and brake lights are on the same circuit on most cars in the 60s and 70s vintage. The common component your turn signals and brake lights share is the turn signal switch. I have seen a faulty turn signal switch cause the turn signal/brake light gremlins you're experiencing.
69 RS, Hugger orange/black, Deluxe interior, Sony AM/FM/XM/CD, PS & PB. 355, forged pistons, Eagle rods, balanced, Iron Eagles, 9.4:1 CR, .038 quench, XR270HR Cam, Z28 intake, FAST-EZ EFI 2.0, Thorley Tri-Ys, TCI 700R4, 2400 stall, 3.42 posi