I think I've found my problem (finally).  The problem is in
'type-enc.tex' I referred to the standard text fonts for
Fourier-Math-Letters and Fourier-Math-Letters-Bold instead of the true
math fonts.  I believe this is how ConTeXt is configured in its
default...  In any case, 'type-enc.tex' should contain:

\starttypescript [math] [fourier] [default,ec]
  \definefontsynonym [Fourier-Math-Letters]         [futmi] [encoding=ec]
  \definefontsynonym [Fourier-Math-Letters-Italic]  [futmii]
  \definefontsynonym [Fourier-Math-Symbols]         [futsy] 
  \definefontsynonym [Fourier-Math-Extension]       [fourier-mex]
\stoptypescript

\starttypescript [boldmath,bfmath] [fourier] [default,ec]
  \definefontsynonym [Fourier-Math-Letters-Bold]         [futmib] [encoding=ec]
  \definefontsynonym [Fourier-Math-Letters-Italic-Bold]  [futmiib]
  \definefontsynonym [Fourier-Math-Symbols]              [futsy] 
  \definefontsynonym [Fourier-Math-Extension]            [fourier-mex]
\stoptypescript


The substitution problem can be seen quite clearly from: 

\starttext

  \loadmapfile[fourier] 

  % Original definition
  
  \definefontsynonym [Fourier-Math-Letters]             [futr8t]
  \definefontsynonym [Fourier-Math-Letters-Italic]      [futmii]
  \definefontsynonym [Fourier-Math-Letters-Bold]        [futb8t]
  \definefontsynonym [Fourier-Math-Letters-Italic-Bold] [futmiib]
  \definefontsynonym [Fourier-Math-Symbols]             [futsy] 
  \definefontsynonym [Fourier-Math-Extension]           [fourier-mex]
  
  \section{Fourier-Math-Letters}
  \showfont[Fourier-Math-Letters]
  
  \section{Fourier-Math-Letters-Italic}
  \showfont[Fourier-Math-Letters-Italic]

  \section{Fourier-Math-Letters-Bold}
  \showfont[Fourier-Math-Letters-Bold]

  \section{Fourier-Math-Letters-Italic-Bold}
  \showfont[Fourier-Math-Letters-Italic-Bold]
  
  \section{Fourier-Math-Symbols}
  \showfont[Fourier-Math-Symbols]

  \section{Fourier-Math-Extension}
  \showfont[Fourier-Math-Extension]

  % What about these fonts?

  \section{futmi}
  \showfont[futmi]

  \section{futmib}
  \showfont[futmib]

\stoptext

Many thanks to those who replied,
Randall
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