The attached schematic shows typical turn signal switching when a dual filament bulb is used for brakes and turn signals.
The front bulbs must be switched seperatly from the rear.
The switching consists of (2) DPDT switches (double pole double throw, maintained).
If your existing switch must be retained, (2) relays could be used in place of the DPDT switches.
General purpose relays will be adequate for this. 12vdc coil with DPDT 10 amp contact rating.