Total resistance across a capacitor in series
Part of the issue is that you asked for the resistance measured across the capacitor without actually understanding what that means.
It means as measured across the two terminals of the capacitor (i.e. you stuck the probes across the capacitor).
It's because when you turn off a voltage source to measure things, you set the voltage source to 0V, and 0V is the same as a short-circuit. If it were a current source, you set it to 0A, which is the same as an open circuit.
What you seemed to have done instead is just pick the terminal of the capacitor that is convenient, and then used ground as the other terminal, and then just kind of ignored R_sig because the voltage supply was in the way.