Or is each photon exhibiting evidence of wave-like behavior even though acting on its own?
Yes, I believe this is the case. The photon approaches the two slits. It's wavelike properties interact with the two slits in such a way that the path it takes after the slits depends on a probability distribution. The detector then detects the photon. The next photon does the same thing, and the next. Eventually, enough photons have gone through the slits and been detected on the other side that the probability distribution can be seen in the pattern of the detected photons. Assuming that the photons are the same wavelength and the orientation of their path relative to the slits is preserved, then each photon will follow the same probability distribution.
It's like running a Monte Carlo simulation in which each photon has a probability of being detected at a certain position and with enough runs the pattern emerges.
However, the two-slit interference pattern is typically taught with just pure wavelike properties, with a "wave front" of light entering the two slits and interfering on the other side. The problem is that the wave model and the particle model are obviously individually incomplete descriptions of the photon (and all elementary particles), and the use of them together is a bit of a kluge, because we don't have a complete model that gracefully handles the duality.