You say you replaced the "gear" oil. Did you replace the transmission fluid (ATF) and make sure the level is correct by following the proper procedure? And is the cooler for the auto trans? Did you check the transfer case oil level as well? How many miles and what year is your FJ?
Also, electrical gremlins may be at work. The way to check that out is to find out what the actual auto trans temp is when the light comes on and see if it's actually too high. You can do this either with a OBDII scan gauge that has the PID to read transmission temps, or obtain a handheld IR thermal temperature gun and point it at the transmission pan and measure the actual temperature.
Cross-checking warning light vs trans temp reported through OBD won't work as they are both reading the same sensor in the transmission.
One way of cross-checking for an electrical/sensor problem is to look at both the pan and torque converter outlet temperatures through the OBD ... under steady-state cruise conditions they should be within a few degrees of each other, and pan temp can NEVER be higher than TC outlet temp.
OP, when you say the AT overtemp light only comes on in 4H but never in 2H, is the vehicle being driven in EXACTLY the same load conditions when comparing 2H vs 4H?
Absolute first thing I'd verify is AT fluid level at operating temp, and verify that the lines to the aux trans cooler aren't pinched or internally restricted by a chunk of debris.
And clarify: you are running BOTH trans coolers in series, hot ATF from the transmission first passes through the in-radiator cooler, and then through your AUX cooler, and then back to the transmission, correct?