You could try to add a debug line to STORE, too: that way, following the process should be easier; in any case, it seems that STORE gets called correctly by tkremote.pl, but that the tie interface is not notified when $wait changes.
Well, I cannot solve your problem, but I might offer you a bunch of CPAN suggestions for a workaround:

• Tie::Watch, implementing "watches" or callbacks over Perl variables (could be the module Tk is using under the hood, dunno)
• Tie::Coupler, to couple scalars together (maybe this module "senses" changes better than Tk?)
• Tie::RemoteVar, a mechanism for sharing variables that should be both easy to use and more portable than the one you're using.

I have not actually tried any of those, but they seem a promising starting point.