What can we do to fix our 96 buick regal?

SOURCE: Turn Signal

The turn signal switch most likely needs to be replaced, and yes the steering wheel does have to be removed to make this repair.

SOURCE: 96 chevy lumina sedan

for both issues, could possibly be the flasher unit for the blinkers.....which could be separate from the hazard flasher unit...(happened on my 92 chevy lumina) or the actual turn signal switch which is located in the steering column....not the stick you push, but the part inside that the lever controls (also happened on my lumina............3 times)

TIP:

start by checking the flasher....its cheap maybe 3-4$ for a new unit.....if thats not it and you figure out its the switch, go to a junkyard.....its wayyyy cheaper

SOURCE: Chevy Cavalier 2001 turn signal blinks fast

If new bulbs don't work, it is probably the harness that holds the bulb. I had to replace both on my car after fighting with the problem for over a year and not knowing.

SOURCE: signal bulb on 2003 buick regal

To change front turn signal –
open the hood; look in back of headlight; two white clips; pull straight up, and then whole headlight comes out including turn signal; it is all one unit; remove rubber cover, then you take bulb out of unit. Mechanism that bulb fits in will need to be turned clockwise (looking from the front) and pulled to get it out of the larger unit holding all lights. Be sure and put rubber cover back on before re-inserting the two white clips.

SOURCE: turn signals flashing too fast

Yes, This is easy. Recall on this problem. Take into dealer for free recall solution and it will stop.