A signal source may well have two or more different output impedances. The most useful one of these is the synchronous output impedance, that is the Thevnin equivalent output series impedance of the source. This is measured without using a network analyser.
Measure the output voltage of the signal source. Now load it with a known output resistor and measure again. Now solve for the unknown output impedance in terms of the known load, using the different voltages.
In order to guard against errors, noisy voltage reading errors, big 'reading what the resistor is' errors, 'output impedance not being constant for some reason' errors, repeat for several values of output load.
Two alternative output impedances are the measurement of the impedance directly with a network analyser, with the generator producing a signal, and with the generator on, but producing a zero-amplitude signal. If the generator is a real voltage source followed by a real resistor, then these two measurement should give the same result as the resistive loading one.
However, some (some audio, most RF) signal generators only emulate a real voltage source followed by a real resistor. If the actual source is levelled by a detector and feedback loop, all sorts of complications could arise, where the probe signal generated by the network analyser interferes with the internal signal the source is making.
While the network analyser measurement may be appropriate for certain applications, the self-measurement with resistive loading produces the correct results to use for measurements where the signal source is used as the source of signals.
The output impedance may well vary with some generator settings. For instance, a generator capable of producing a wide level range might have a very consistent output impedance on all the lower ranges, where an attenuator is switched into the output, but have a poor impedance on the top range, when the attenuator is bypassed for MOAR POWA.