The silver square box pictured on your lower dash panel is the headlamp delay module . Btw , the black plastic box is the wiper delay module. The ignition switch that SteelHeadz wants you to temporarily remove for test purposes is along the steering column . You will have to climb into your favorite contorted upside down position and get comfy ( don't forget a flashlight ) . Look on the steering column where it goes down toward the firewall . On the top of the tube you will find a switch with 12 & 14 gauge wiring plugged into it. You should find two small screws securing it to the column. Before you loosen it , try to mark its position so it stays in adjustment . Scribe marks on the corners where you can find them later upon reassembly. Btw , do not OVERTORQUE the mounting screws as the threaded holes WILL strip ! Please use restraint . As SteelHeadz wanted you to do , now remove the ignition switch so the link rod is free to move independently. You will not have to remove any wiring but if you fear shorting any connections , it's always safe to disconnect the battery negative. Now as previously prescribed , see if the ignition lock cylinder will rotate. If it does not :???: , reassemble the ignition switch as the problem is in the upper column as SteelHeadz posted. It's been a while so I totally welcome SteelHeadz to lead should I miss direct. For the next procedure , you will have to peel the steering wheel back off again ( sorry) and be prepared to go deeper. Hope you have a lock spring compressor to get the snap ring and lock plate off. You may have to climb back under and pop off the turn signal and wiper switch harness connector from the steering column tube. Should have mentioned that when you were working on the ignition switch. You want to try to give slack to the turn signal switch assembly so as not to damage any wiring. Trying to avoid total removal of wiring harness for you as it can be VERY tedious . You just want some slack. Carefully disassemble all parts noting where to reassemble later including the ignition lock cylinder. You are going to remove the steering column upper housing to get a good look at the cam gear and related parts SteelHeadz spoke of in his post to you . This is where we must find what the problem is. I couldn't personally say if you'll luck out and find a stuck ignition switch and simplify this repair but it's likely the cam gear or rack that engages with the link rod to the ignition switch is damaged. Hope not because I think this requires further disassembly. That will require unloading the tilt column spring ( not too scary) and removal of the tilt column pivot pins. You will need the right tool to extract the two pins as using a cheap screw with a make shift Rube Goldberg puller ( like I'm famous for) will undoubtedly break off. I own one after proving that theory correct and you'll have to get one off a tool truck or online . If lucky , maybe a good mom and pop parts store will carry one like I was fortunate to find since pep bays , autozone , advance etc. will not likely have one. Don't think I'd trust their tool quality anyway. Mine is an OTC part # 7889 if you need reference.
Lets hope for the best and your repair does not go this far but the experience is fun as always.
Post back your findings and hoping I made SteelHeadz proud . He's the man , I'm just working up to shining his shoes . Lol