If they both quit at the same time, then probably the Fuse. They are on the same circuit IIRC.But;The rear sockets need to be grounded back to the battery, so it could just as easily be the ground.
But;If the front turn-signals light up but do not flash,then it's probably a faulty Turn-signal switch in the top of the column.
And if all the turn signal bulbs illumine (2+2)but do not flash, then replace the flasher. If that don't do it, then check the grounds;again.
But make sure the brake switch is working before tearing down the column.
All the power for the rear brakelites/signals is routed through the signal switch. I have seen a few melted signal switches, and then nothing connects anymore.....