I know there were TSR-like routines in the days of the Radio Shack and
Epson 10 computers and later Superbrain computers because I used such
things with CP/M.
I know that in the Epson CPU I had to set up a background module to
handle the USA -type keyboard in Spanish. There was something similar
in the Burroughs B22 BTOS software. These are, I think all pre-1986. Of
course they didn't use the interrupt structure servicing the same way
as DOS later did, but the similar hardware was there in the 8086 chip.
(Yes I just located a BTOS assembler manual dated Feb 1986. Somewhere
I have a complete CPM source listing). I seem to remember that
creating a TSR was a service call in DOS 3.1 (whenever that was) and
possibly earlier versions.