The problem was that the directory I specified for $(INST_ARCH) was different to $(ARCHNAME), as determined by the GNUmakefile.
I still don't know whether that *should* lead to @INC being empty ... but I know from experience that it certainly does.

If you're wondering what happens when such a mismatch occurs, gmake install puts the architecture-specific stuff into the directory specified by $(INST_ARCH), not the directory specified by $(ARCHNAME).

There's no problem if (and only if) either:
1) $(INST_ARCH) is unset (undef);
or
2) $(INST_ARCH) is set to $(ARCHNAME).

I don't really see why it should matter. Everything would be fine if @INC was set in accordance with $(INST_ARCH).
If it's so important that this not be allowed, then maybe it ought to be stated clearly that, when $(INST_ARCH) is set, it must be set to $(ARCHNAME).

Cheers,
Rob