We outline the design of beam experiments for the electron linac at the Fermilab Accelerator Science and Technology (FAST) facility and for the Integrable Optics Test Accelerator (IOTA), based on synchrotron light emitted by the electrons in bend dipoles, detected with gated microchannel-plate photomultipliers (MCP-PMTs). The system can be used both for beam diagnostics (e.g., beam intensity with full dynamic range, turn-by-turn beam vibrations, etc.) and for scientific experiments, such as the direct observation of the time structure of the radiation emitted by single electrons in a storage ring. The similarity between photon pulses and spectrum at the downstream end of the electron linac and in the IOTA ring allows one to test the apparatus during commissioning of the linac.