If the dash only has one light, how do you have it connected to the harness?
Typically you would have two bulbs connected to the two indicator wires. If you connected those together, tou have shorted the front turn signals together and both of them will flash at the same time.
A single indicator should be wired between the flasher and the steering column connector so that it flashes with either signal, but doesn't short them. Alternatively you could connect the two indicator wires together with diodes to prevent back-feeding power.
Can you give us a simple "what bulbs do what in each switch position" to make sure we are on the same page?
Something like:
Turn signal left, brakes not applied:
Front left turn bulb on
Front right bulb off
Rear left brake/turn bulb flash
Rear right brake/turn bulb off
Dash indicator off
Turn signal left, brakes applied:
Turn signal right, brakes applied:
Turn signal right, brakes not applied:
Turn signal center (off), brakes applied:
Also, is the turn signal switch the original one in the column? Or is it an aftermarket one?
How many wires do you have going into the column?