Would Maxwell or his contemporaries have known or thought that electricity and electrical phenomenon are made up of transverse waves instead of longitudinal ones prior to his paper that light was a transverse wave?

 My answer on Quora.

Yes they would have. The best evidence that we have that Light is a Transverse wave is that fact that it can be polarized so that the electric field of the EM waves oscillate along one plane. Polarization cannot take place with longitudinal waves such as sound as the transmission direction is the same as that of the disturbance causing the wave. In transverse wave transmission directions are perpendicular to the disturbance and c

Source: Socratic

People have been aware of the phenomena since the age of the Viking. Etienne Louis Malus (1801) showed hope light intensity follows a square drop off law that is related to the angle of rotation between two polarization sheets. Sir David Brewster (1812) further showed how surface reflection at a specific angle (the so-called Brewster angle) can produce polarized light (of use in kaleidoscopes).

The Brewster Angle (Theta B) is the angle of incidence that provides for reflected polarised light Source: This Condensed Life