I should have waited a bit longer before posting. I found the answer.

The event to bind is Configure.

Just bind a callback to a Configure event on your widget, and you can reconfigure as you please.

What surprised me was that I could call the widget's configure method in the ConfigureConfigure callback without creating infinite recursion.

The code below shows the technique.

use strict;
use warnings;


use Tk;

my $mw = MainWindow->new();

my $long_text = <<EOT;
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Pellentesque
+ dictum tempor augue. Sed id pede. Suspendisse a erat a risus tincidu
+nt rhoncus. Integer eget risus. Nulla nunc odio, viverra eget, consec
+tetuer non, mollis at, felis. In hac habitasse platea dictumst. Nulla
+ accumsan volutpat eros. Vivamus convallis, eros ut convallis facilis
+is, justo ipsum convallis orci, vehicula laoreet purus eros eget ante
+. In tempor. Proin varius placerat nisl.

Class aptent taciti sociosqu ad litora torquent per conubia nostra, pe
+r inceptos hymenaeos. Aenean pretium augue ac nulla. Praesent ante ri
+sus, iaculis et, malesuada a, luctus in, orci. Sed erat odio, auctor 
+sed, molestie vel, volutpat at, elit. Phasellus fermentum ultricies e
+st. Aenean interdum elit sit amet est. Donec luctus lacus a turpis. S
+ed et risus. Fusce metus. Pellentesque lorem dolor, volutpat in, cong
+ue id, luctus et, magna. Nullam congue sagittis orci. Pellentesque ne
+c metus. Nulla nulla.

EOT

my $l = $mw->Label( 
    -text => $long_text,
    -wraplength => 250,
)->pack( 
    -fill => 'both', 
    -expand => 1,
);

$l->bind( '<Configure>', => [ \&ResizeMe, Ev('w') ] );


sub ResizeMe {
    my $l = shift;
    my $w = shift;

    # Amazingly, this does not lead to infinite recursion.
    $l->configure( -wraplength => $w );
}

MainLoop;
[download]

Update: I forgot to mention, that I figured this out by looking at the Tk::bind POD. The section called "BINDING CALLBACKS AND SUBSTITUTIONS" includes an entry for the 'w' character which returns a width for an event. The event list includes Configure, as does the h/height entry. So, I figured, maybe Configure events are generated when a widget is resized. I tried a quick binding and it worked.