Makefile rules have now been adjusted. Please download the latest trunk version of the source code (perhaps from https://sqlite.org/src/tarball/trunk/sqlite-trunk.tar.gz) and rerun your "./configure && make install DESTDIR=..." or whatever it was that you were trying to do and let us know if it is working for you now. Thanks!

Thanks. To comment on specific issues:

#1. Respecting --with-tcl: it works good enough although I think the if should be guarded additionally by "" eq $with_tcl:

    if {$use_tcl} {
      if {[catch {exec $with_tclsh $top_srcdir/tool/find_tclconfig.tcl} result] == 0} {
        set with_tcl $result
      }
      if {"" ne $with_tcl && [file isdir $with_tcl]} {
        msg-result "$with_tclsh recommends the tclConfig.sh from $with_tcl"
      } else {
        proj-warn "$with_tclsh is unable to recommand a tclConfig.sh"
        set use_tcl 0
      }
    }

#2. Respecting TCLLIBDIR -- still missing. sqlite installs to first path from $auto_path which is not the path that I'd like it to install to

# T.tcllibdir = shell code to extract the TCLLIBDIR to the tcllibdir
# shell var and exit with !0 if it cannot be determined. It must be
# part of a chained series of commands so that the var survives for
# the following rules in the same recipe.
#
# Algo: tcllibdir = the first entry from TCL's $auto_path which refers
# to an existing dir, then append /sqlite3 to it.
#
T.tcllibdir = \
    for tcllibdir in `echo "puts stdout \\$$auto_path" | $(TCLSH_CMD)`; do \
    [ -d "$$tcllibdir" ] && break; done; \
    if [ x = "x$$tcllibdir" ]; then echo "Cannot determine TCLLIBDIR" 1>&2; exit 1; fi; \
    tcllibdir="$$tcllibdir/sqlite3"; echo "TCLLIBDIR=$$tcllibdir"

#3. Respecting $(DESTDIR) -- works fine

Respecting TCLLIBDIR -- still missing.

After looking over the legacy configure script, i see that it used to honor whatever override TCLLIBDIR was set when configure was run. We no longer do that check at configure-time because that makes it onerous to communicate the TCL-related configuration to static/hand-written makefiles (which we have a few of outside of the source tree).

However, as of a moment ago, in the current trunk you can override TCLLIBDIR when running make or as an environment var:

$ m libtclsqlite3.so
...
TCLLIBDIR=/usr/share/tcltk/tcl8.6/sqlite3
+ ccache ... libsqlite3.so ... -Wl,-rpath,/usr/share/tcltk/tcl8.6/sqlite3

$ rm libtclsqlite3.so 

$ m libtclsqlite3.so TCLLIBDIR=/foo/bar
TCLLIBDIR=/foo/bar
+ ccache ... -o libtclsqlite3.so ... -Wl,-rpath,/foo/bar

$ rm libtclsqlite3.so 
$ TCLLIBDIR=/bar/baz m libtclsqlite3.so 
$ ccache ... -o libtclsqlite3.so ... -Wl,-rpath,/bar/baz

In addition, i will investigate re-adding the option to bake it into the build at configure-time, noting that we still need the option of doing it at make-time (using the T.tcllibdir bit you quoted) for the sake of our static/hand-written makefiles.

will investigate re-adding the option to bake it into the build at configure-time ...

The trunk once again supports that:

$ ./configure TCLLIBDIR=/this/is/my/place
...
$ m libtclsqlite3.so
...
ccache ... libtclsqlite3.so tclsqlite.o ... -Wl,-rpath,/this/is/my/place

And it can also be overridden at make-time.