I looked in my factory book for a 1990, did not see that part but the diagrams in the book dont show everything. however found this...
https://www.fixya.com/uploads/images/7_20_2012_11_14_04_pm.jpg
it is from a 1990 Wrangler. the "ignition switch actuator rack" looks simular to the part you showed. Not the same, but simular.
Does everything work on yours with that part not in it? will jeep start? accessory position? does the ignition lockout if tranny not in Park? do the signals work, do signals self cancel after a turn? hazard lights, cruise control, horn, wipers, washers, high beams, etc... function as normal? check all the steering column functions, as likely one or more of them wont work with that part missing. that will help you identify it by knowing what function it effects when missing.
good luck.
ps also when reassembling, remove old grease and dirt on the sliding , rotation, cam surfaces, then regrease with clean plastic compatible dielectric grease. use dielectric grease so that it wont cause a short circuit the grease bridges over electric contacts.
the lock cylinder should be lubed with dry graphite, "key lock lubricant". blow it into the key hole and then work the key in and out/ rotate to work the graphite in. Graphite is conductive so only use in the lock cylinders while you are at it, lube the other key holes on doors and hatch , then do your house door locks. this should be a yearly thing on your car(s), house, and Jeep locks.