Download the Factory Service Manual for your year from the link below and use Adobe Reader to keyword search through it. In it you will find the correct wiring diagram for your year along with the locations of all the harness connectors. With the wiring diagram and the circuit specific diagram already included in this thread, you should be able to follow the electricity through the circuit.
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When you "switched" the circuit and the fans cam on, how did you do that? Did you apply power or ground to the relays? ...or something/somewhere else?
Also, there are actually codes for failure of the low and high speed cooling fan circuits. Does your Check Engine AND SES lights both illuminate during bulb-check when the key is first turned from OFF to RUN? If not, SCAN that PCM, you probably have a code waiting.
If the CE and SES bulbs illuminate during the bulb/system test, and manually switching the fans got them to run, it may just be possible you're not hitting the first temperature threshold for the fans to come on.
I live in West Central Florida, both my LT1's are running below fan temps so far. I drove around for an hour yesterday in my C4 and never exceeded 221F, so my fans never spun up. Completely normal!
Also, with the low/high speed setup you have, both fans come on low speed (half-voltage) and if needed switch to high speed (full-voltage). When the hood is closed, it's impossible to hear the fans on low, and if the hood is open, it's still extremely hard to hear them kick on. Even the switch to high-speed isn't too noticeable with the hood closed.
If the cooling system is performing as it should, high-speed fan activation is really uncommon unless it's extra nasty outside, or you turn on the A/C. Usually, low-speed is enough (even sitting idle) to bring temps down and cut the fans off.
Are you even overheating? If your temperature needle is going high but the engine isn't getting sluggish, it's more likely your temp gauge is getting bad readings from the sensor in the head. The temp gauge has absolutely nothing to do with fan operation, it's there for your eyes only. The PCM controls the fans based from a sensor on the water-pump.
Of course, there's the fact that even the slightest amount of air in an LT1's cooling system greatly impacts efficiency. Fans could be operating as designed, the system could be 100%, and a little air will in the system will affect it like there was no coolant at all. If you've never bled the cooling system, try it. If you have but suspect you didn't get all the air out, elevate the front end so that the bleed screws are the highest point and try again. Sometimes it's necessary to do that.
Good luck!