Also passenger airbag off light on rearview mirror stays on too and lock symbol on dash stay lit when vehicle is locked with key remote.
Check engine light comes on and stays on after engine has been turned off. on 2005 Buick Rainier
This could be a body computer issue. Not at work where I can research today. Suggest you try disconnecting a battery cable for about 10 min. just so all the modules can reboot. May be Monday before I can follow up.