  Test beam facilities are essential to study the response of novel detectors
to particles. At the DESY II Test Beam facility, users can test their detectors
with an electron beam with a momentum from 1-6 GeV. To track the beam
particles, EUDET-style telescopes are provided in each beam area. They provide
excellent spatial resolution, but the time resolution is limited by the rolling
shutter architecture to a precision of approximately 230 $\mu$s. Since the
demand on particle rates -- and hence track multiplicities -- is increasing
timing is becoming more relevant. DESY foresees several upgrades of the
telescopes. TelePix is an upgrade project to provide track timestamping with a
precision of better than 5 ns and a configurable region of interest to trigger
the telescope readout. Small scale prototypes have been characterised in
laboratory and test beam measurements. Laboratory tests with an injection
corresponding to 2300 electrons show a S/N of above 20. Test beam
characterization shows efficiencies of above 99% over a threshold range of more
than 100 mV and time resolutions of 2.4 ns at low noise rates.
