Standard signal processing approaches for scintillation detectors in positron emission tomography (PET) derive accurate estimates for 511 keV photon time of interaction and energy imparted to the detection media from aggregate characteristics of electronic pulse shapes. The ultimate realization of a scintillation detector for PET is one that provides a unique timestamp and position for each detected scintillation photon. Detectors with these capabilities enable advanced concepts for three-dimensional (3D) position and time of interaction estimation with methods that exploit the spatiotemporal arrival time kinetics of individual scintillation photons. In this work, we show that taking into consideration the temporal photon emission density of a scintillator, the channel density of an analog silicon photomultiplier (SiPM) array, and employing fast electronic readout with digital signal processing, a detector that counts and timestamps scintillation photons can be realized. To demonstrate this approach, a prototype detector was constructed, comprising multichannel electronic readout for a bismuth germanate (BGO) scintillator coupled to a 4x4 SiPM array. In proof-of-concept measurements with this detector configuration, we are able to count and provide a timestamp for all optical photons produced by 511 keV photoelectric interactions. We show that this photon counting detector concept can implement 3D positioning of 511 keV photon interactions and thereby enable advanced corrections for time of interaction estimators. We outline the methodology, readout, and approach for achieving this detector capability in first-ever, proof-of-concept measurements for scintillation photon counting detector with analog silicon photomultipliers.