We study age-agnostic scheduling in a non-preemptive status update system with two sources sending time-stamped information packets at random instances to a common monitor through a single server. The server is equipped with a waiting room holding the freshest packet from each source called "single-buffer per-source queueing". The server is assumed to be work-conserving and when the waiting room has two waiting packets (one from each source), a probabilistic scheduling policy is applied so as to provide Age of Information (AoI) differentiation for the two sources of interest. Assuming Poisson packet arrivals and exponentially distributed service times, the exact distributions of AoI and also Peak AoI (PAoI) for each source are first obtained. Subsequently, this analytical tool is used to numerically obtain the optimum probabilistic scheduling policy so as to minimize the weighted average AoI/PAoI by means of which differentiation can be achieved between the two sources. In addition, a pair of heuristic age-agnostic schedulers are proposed on the basis of heavy-traffic analysis and comparatively evaluated in a wide variety of scenarios, and guidelines are provided for scheduling and AoI differentiation in status update systems with two sources.