What electrical attributes determine if signals from a signal generator can penetrate objects?
Actually all signals are in the space around the conducting metal, the metal only force the fields by stating a boundary condition. Only the resistance of the wire generates some field in the metal, but if the losses in the wires are low as percents of the transferred energy, the main part moves outside the metal. Some special constructions exist to keep the signal inside metal- They are coaxial cable and waveguide (=tube) also in these the signal is between the metal walls.

We, practical electricians, very likely throw the preceding story out of our minds because in many practical cases we can follow the fields in the space with only two numbers. They are the voltage between the wires and the current in the metal. But microwave engineers have not that luxury. Their fields are often not reduceable to be followed with voltage and current. It's possible only with waveforms called TEM. They exist around parallel conductors where the the cross-section pattern is constant along the wire length (coax, pair cable, twisted pair)

The special things in TEM is that the energy propagates around the wires but it happens along the wire without spreading into the space, the energy can be directed to a load. Wires for TEM do not act as antenna like spaghetti wiring. The antenna action of non-parallel wires becomes apparent when the wire length is 10% or more of the wavelength.