VDE limits 1/4" Faston to 20A and I have seen up to 40A in automotive parts but I find 25A is reasonable. At 30A up things are pretty hot. It should be fine for headlights or fog lights at 20A.
Every connection has resistance and will make heat, the datasheet spec is missing because it depends on how much heat you can get rid of. If the connector is under the hood near the engine, at a relay pin, or is wrapped in insulation (tape, wire loom etc.) it will get hotter and the wire melts.
Cheap chinese crimp connectors have very thin metal, so be careful to not use them for high currents.
13AWG is pretty stiff to use and it can tug and bend the Faston, with vibration. Blue is 14-16 ga. I would try the yellow ones.
Fastons are terrible to make waterproof, so I use Deutsch or Delphi/Packard connectors.