Swap that relay out for another one of the same rating that you know to be good and take it for a short drive again. Check your owner's manual and find one that's optional (not used, stereo, windows, heated seats, etc).I'm not sure how to take that plug apart to examine it. I bypassed that one burnt looking pin (cut that green/white wire on both the male & female connectors & connected them with a new piece of wire).
In doing so, the pump now comes on when I jump it at the fuse box relay. However, when I replace the fuse it doesn't seem to automatically come on. Just took it for a small drive and IAT2 ramped up to 180 in a small distance of easy driving.
Drove it back home, popped the hood and the pump is not running. Cut the car off, removed the pump relay & installed a jumper wire, pump came on.