Hi,
I hate to say this but it sounds like a bad Ignition switch.
The Ignition switch is a double throw switch. What that means is, for example, take everything that is normally on with the switch in the RUN position. Out of those devices, some are also powered in the ACC position. Therefore, the devices that are powered only in RUN are on a different pair of contacts in the switch than the devices that are powered in both the ACC and RUN positions.
These devices (should be) all on the same circuit in the ignition switch:
- Radio
- Cigarette Lighter
- A/C Blower Fan
- Turn signal flasher
- rear wiper/ washer
What you need to do is find the wire coming out of the ignition switch for these devices (in cherokees it is a #12 AWG brown wire) and see if it has power both in the ACC and RUN positions. This will tell for sure one way or the other.
-Nick

__________________
1988 Jeep Cherokee w/ 410,000+ miles. Now a
100% Electric Vehicle!
NO Gas, NO Emissions, NO Problem! --
http://www.DriveEV.com/