We usually refer to it as the turn signal stalk, but it's technically a multi-function switch. Each independent of the other.
There's the cruise function, which is a tiny printed circuit inside the stalk. Cruise is the only circuit in the stalk. Then there's the turn signal switch, which functions only in an up and down motion and isn't actually a part of the stalk. Next is the dimmer switch, which functions in a front to rear motion and is internal to the column. Wipers are controlled by a rotational switch which is what the multi-function switch snaps into. They are actually controlled by the motor and circuit board underneath the front hood. Any one of them can fail or work without affecting the others. Let's work on the turn signals first, since those are needed.
The turn signal flasher is clipped to the left hand side of the steering column support. You will need to remove the lower column trim plate to access it easily.
Check all the bulbs using the 4-way flasher. If any of them are out, including any of the side markers, it can cause them to not function. This is a test of the bulbs, only. The 4-way and turn signals are actually on a different circuit. Check all fuses. Pontiac had a way of powering things off fuses that were marked for other purposes. BAT fuse is a common one. Also Radio.
An initial check of the cruise circuit can be done by turning off the cruise. Slide the switch toward the end of the stalk. Have a helper turn on the ignition then move the slide switch toward the steering column. At the same time, place your hand on the small solenoid located at the end of the coffee can in the engine bay. It's on the left trunk wall. The solenoid has an orange harness plugged into it. It should click. If it doesn't, something within the circuit is faulty.