Have a look and see if you have a fuse or relay that controls the EFI / fuel pump. It is very unlikely because of the power requirements, it will be fed directly from the ignition switch.
If you are having problems with the marker, tail and license plate bulbs not working, these should work without the ignition switch being on.
If it is turn signals you are having problems with, try depressing the emergency hazard warning switch, does that work and all turn signals work? That should also work without the ignition switch not being on. The hazard switch itself does sometimes fail, hopefully it is just a fuse, this is a quick test to get you in the right direction.. Pun intended..
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