The electric fan, just behind the grill, is not a engine cooling fan although I suppose it helps a bit when it's running. That fan, like all similar fans, is there to force air across the AC condensor so your AC will cool properly. Hence it trips on/off and high/low based on AC sensors, don't ask me what sensors or where although this post might help
viewtopic.php?f=5&t=67046 or send him a PM. If the fan doesn't run try applying power directly to see if 1) motor burned out; 2) relay bad if it runs that way then likely the switch(s) associated with the AC system that trigger the fan have issues or perhaps your AC is low on charge is about all I can offer.
Mechanical fan is what provides max engine cooling and the OEM fan clutch is 1) known to fail and 2) if working kicks in IIRC at an engine temp on the order of 2225+F well up into an over heat curve. The Hayden 2905 with or without the OEM plastic fan is much stronger and kicks in at an engine temp more like 200F just at the start of an over heat curve.
PS with a garden hose check your AC condensor/intercooler/radiator package to be sure the fins are not clogged and air can flow freely.