Lightweight test for bimodal distributions?
An easy way, especially one that is used in the detection and SNR estimation of PSK signals in a noisy signal, is based on stochastic moments of the received amplitude:

The kurtosis can be used as measure of how little "centered" a symmetric distribution is.

You could calculate a sample kurtosis frequency bin-wise in your spectrogram; those bins with high curtosis are likely to contain more than just Gaussian noise.

In a slightly more elaborate version of that algorithm optimized for detecting 2-FSK, you could use that to identify "candidate bins", subtract their mean power to have zero mean variables, and then calculate the covariance of pairs of these (i.e. calculate a covariance matrix). You're looking for a strong negative covariance – whenever one bin has above-average power, the other has low power.