Assuming this is a 72ish duster (profile pic.) Then the TS flasher and 4 way flasher are separate circuits until they reach the TS switch. Also they need to flow some current to make them flash, if you have switched away from OE bulbs then they may not use enough current to make them blink. Also the circuits themselves could have to much resistance like corroded sockets as stated by 67Dart273, or the flashers themselves could be bad. If the indicators still work when the flasher is pulled out then you have a shorted TS switch.
