~/.localtime ?

[Roland McGrath]

Running programs are not going to be reliably affected unless you provoke
them to call tzset or equivalent, anyway.  Having things stat'ing a file
implicitly all the time just to see if it changed is not viable because of
the performance hit and unwanted exposure to filesystem flakiness.  So I
don't think you can reasonably get what you're after this way.  Having
things refer to a new file implicitly has all sorts of other complications
wrt security concerns and so on.