TimeoutHandler was starting the Timer when the handler was created,
instead of when serving a request. It also was sharing it between
multiple requests, which is incorrect, as the requests might start
at different times.

Store the timeout duration and create the Timer when ServeHTTP is
called. Different requests will have different timers.

The testing plumbing was simplified to store the channel used to
control when timeout happens. It overrides the regular timer.

Fixes #14568.

Change-Id: I4bd51a83f412396f208682d3ae5e382db5f8dc81
Reviewed-on: https://go-review.googlesource.com/20046Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>