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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 $μ$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.