Andy unless you have excessive pressure in your cooling system (due to a blowing head gasket) you shouldn't ever have steam coming out of that hose . . . . so if it's not a BHG it may be the Radiator Cap as has already been suggested.
It is a special dual design, as when cooling down it opens to allow coolant to be sucked out of the overflow tank back into the radiator (if it needs it) . . as well as of course acting as a safety valve and opening if excessive pressure builds up
By the way, have you not found the UK Mk3 Supra Forum?
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1991 3.0i (N/A) Manual, Black Mica. Owned 6 yrs, Mint Bodywork, Daily Driver. Recent Engine Recon (rebored, crank ground, new oil & water pumps etc), New Rad & Catless Exhaust, EGR all removed, Inline PCV Filter (Photos at http://wessexproductions.co.uk/supra )
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