Wrench light comes on but trips no codes. When this happens my reverse lights come on and stay on even in drive

When a warning light comes on, there's a code stored in the computer....always. There are generic codes that inexpensive code readers can read and there are manufacturer specific codes that require very expensive professional scan tools. If you didn't use a pro scan tool, that's why you're not seeing the code. Computers don't turn on the light for no reason at all.

I have a similar issue ('05 base Freestyle), without the reverse lights. It seems to come on consistently during cooler temps - around 60 deg and below. Rarely will it light up in the summer. It's usually after running the engine for a couple of minutes. It stays on for 5 to 15 minutes and goes away. Stopping and restarting usually clears it, but no 100% of the time. The car runs normally without any performance issues. On rare occasions, the light will flicker as I alternating between accelerating (off) and coasting (back on). But the other night, it flickered while I was parked. The biggest reason for replying to this: My Ford dealer had their laptop hooked up to it while the light was lit - no code was thrown. If Ford's own software can't see a code, it makes repairs a bit difficult. The dealer said they could start replacing parts based on their best guess, but fully admitted that wasn't a wise strategy. Without a code, they would know a good starting spot either. While pouring over forums, the throttle body was a popular suspect. I replaced it, retrained the comupter, but still no dice.