The Jargon File (version 4.4.7, 29 Dec 2003):

mode bit
 n.

    [common] A flag, usually in hardware, that selects between two (usually
    quite different) modes of operation. The connotations are different from 
    flag bit in that mode bits are mainly written during a boot or set-up
    phase, are seldom explicitly read, and seldom change over the lifetime of
    an ordinary program. The classic example was the EBCDIC-vs.-ASCII bit (#12)
    of the Program Status Word of the IBM 360.


The Free On-line Dictionary of Computing (30 December 2018):

mode bit

   A flag, usually in hardware, that selects between two
   (usually quite different) modes of operation.  The
   connotations are different from flag bit in that mode bits
   are mainly written during a boot or set-up phase, are seldom
   explicitly read, and seldom change over the lifetime of an
   ordinary program.  The classic example was the
   EBCDIC-vs.-ASCII bit (#12) of the Program Status Word of the
   IBM 360.  Another was the bit on a PDP-12 that controlled
   whether it ran the PDP-8 or the LINC instruction set.

   [Jargon File]