Closed photon orbits around isolated black holes are related to important aspects of black hole physics, such as strong lensing, absorption cross section of null particles and the way that black holes relax through quasinormal ringing. When two black holes are present-such as during the inspiral and merger events of interest for gravitational-wave detectors-the concept of closed photon orbits still exist, but its properties are basically unknown. With these applications in mind, we study here the closed photon orbits of two different static black hole binaries. The first one is the Majumdar-Papapetrou geometry describing two extremal, charged black holes in equilibrium, while the second one is the double sink solution of fluid dynamics, which describes (in a curved-spacetime language) two "dumb" holes. For the latter solution, we also characterize its dynamical response to external perturbations and study how it relates to the photon orbits. In addition, we compute the ergoregion of such spacetime and show that it does not coincide with the event horizon.