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How important are steering stabilizers, my truck is missing it. I don't know why someone would take it off, but apparently the PO did for some reason. I can see part of the old bracket on the drag link.
A steering stabilizer is intended to dampen/absorb the shock created by the tire/wheel contacting an object that could induce a quick and unexpected steering wheel reaction.
With near stock size tires and stock springs the ~$20 stock replacement stabilizer from Rock Auto works fine for me ('78 F250 4 WD). Not sure about the "don't run without it" part... but I would go ahead and replace it.
I did not have one on my 73 & 77 highboys with manual steering and 36s. I ran my 78 Bronco with 35s without it for 14 years and my current 79 with 33s for 12 years. Just make sure you keep your tires balanced. That helps ALOT.