Non-constant time rate

Supposing you live in Magic Land (tm) and with the technology of early
20th century, and you encounter a zone where time doesn't "flow"
regularly - call it a temporal anomaly or something like that. Could you
detect it?

Here are the rules:
- a Newtonian universe (relativistic effects don't exist; speed, energy
can increase indefinitely)
- "space" behaves usually - distance of 1m is always 1m, no warping here
- time is messed up: it still monotonically flows forward, only
sometimes slower sometimes faster. This is very tricky - your clocks,
observed locally, are always correct, but the time is different when the
outside of zone is used as a referrence.
- you cannot compare objects (clocks, etc.) from within and without the
zone because of handwaving reasons. You have to work within the zone.
- in the long run, time behaves regularly (e.g. if you measure enough of
time within and without the zone, for some large amount of "enough",
they will match; only within the zone it's sometimes slower sometimes
faster.). This rule is actually optional :)

Could something like this ever be detected?

I have a hunch that maybe something with pendulums and relying on the
fact that space is consistent could be the right direction, but I don't
really know where to go with it.