Planes were leaving contrails over WWII Europe. At a great enough altitude, air condensation resulting from the compression of air at a wingtip freezes and leaves a contrail that lasts. Modern jet engines produce particulate matter as a natural result of burning fuel. That further enhances the condensation.
I live right under the flight path into Detroit Metro and see contrails when the weather is right. When the sun is high they don't seem to last as long. At sunset they catch the light for a long time and with the ground getting darker they appear even more visible.
The composition of contrails is chiefly water vapor from the combustion of fuels. Fuels also leave some particulate in the exhaust, particularly jet fuels. This may facilitate a phenomenon similar to cloud seeding where the water condensate may form or propogate a cirrus cloud. These are typically called persistent contrails.
Generally wingtip vortices cause low air pressure which allow water condensation in the low pressure zone. Typically these dissipate quickly as the ambient air pressure returns to the affected area.
You also correctly pointed out that viewing angle and angle of incidence of a light source (typically the sun) can also affect the visibility of contrails.