strange toyota intake position

im confused about my corona, its the 82 model with the 21r-c 2 litre carburettor motor, i think, or fuel injection, but anyways off the tip of the air cleaner disc there is some bendable plastic hosing that goes accross the engine bay and gets ducted outside the engine bay on the right hand side just beneath the front quarter panel? What was this for because it is on 99% of the corona engines of the time, was it some form of factoy cool air intake as all my other carbie running cars just sucked air in from the engine bay.

Its nearly always preferable to source air from a cooler source. Different engine designs and their strengths/shortcomings allowed for different sources, but the fact that its missing on 1% of the Coronas you've seen means that it finally disintegrated or just fell off and the owner didn't replace it.

Its all a matter of how they run. Many GM cars pulled air from around the exhaust manifold until the engine warmed up, then it pulled it from under the hood at the end of the snorkel. Some GM cars pulled air exclusively from the inner fender, like GM TBI trucks. It all has to do with emissions, fuel economy, cold running characteristics, and other operations that the design presents to the manufacturer during R&D