steering wheel has to be pulled off and then you can take the top cover off the steering column to get to the screws that hold the switch in.
hi-beam switch is faulty
Check the dimmer switch and the electrical connections.
Check the fuse for the low beam headlight circuit or possibly a faulty selector (on the steering column) switch.
On the arm with your Main beams switch on. You push it in towards steering wheel
Check bulbs Could be bad switch (hi-lo)
is a switch to change to low beam is located under the emergency brake
Pull the turn signal switch towards the steering wheel to activate high beams.
Which plastic part inside the steering wheel did you replace? The turn signal switch? High/Low beams are controlled by a small switch mounted to the left side of the steering column. You may need to adjust it properly, so that the metal rod comes in contact with the switch, and pushes it far enough to engage (but not too far to bottom out).
My car has a lever on the right side of the steering column that you pull toward to dim. My old car had a switch on the floor that you pressed with your foot.
I have a 98 camaro and it has the same problem. I found that if i took off the top cover for the shifter i can push down on the housing and my high beams will come on.. I found a small plastic piece that came off. Try opening and looking. I heard that alot of camaros have this problem. The switch goes bad. The 96 Camaro's high beams wires do not run anywhere near the shift lever that is on the floor of the 1996 Camaro. It is built into the turn signal selector which is on the steering column. Your problem is either your relay (under the hood in the little box on the driver's side, you have to remove the top to access it) or your turn signal selector. Does the turn signal selector click when you pull it back? If it does click you probably need a new relay. If it does not click you will need to pull the steering wheel to get to that selector and change it. Also look behind the turn signal selector there is a small wire connector that if it comes loose your high beams and cruise control will not work. Often you can connect these wires and get everything back. http://camaroforums.com/forum/93-02-general-41/high-beam-issues-58085/
You will have to pull the steering wheel off and then take the top cover off the steering column and then you can get to the bolts that hold the switch in, you will need a new switch.
Check the fuse for the high beam headlight circuit or possibly a faulty selector (on the steering column) switch.