My understanding is that the standard deviation of the Gaussian window in a Gabor filter dictates the temporal resolution.
Wouldn't it always be better then to make the window smaller, thus achieving a high temporal resolution of exactly when in the input signal the frequency of interest (equal to the frequency of the sinusoid in the Gabor Filter) occurs?
If your gaussian window width goes to zero, you are, in essence, sampling the signal, $x(t)$, (that was multiplied by the complex exponential, $e^{j 2 \pi f_0 t}$, which always has a magnitude of 1) with a dirac impulse. So the value, after integration, is equal to your instantaneous sample with a known complex phase attached to it.
The output of the Gabor filter will essentially be the output of a one-sided AM modulator.
$$ y(t) = x(t) \cdot e^{j 2 \pi f_0 t} $$
