would guess it maybe something to do with preventing combustion gases getting into the air con system?
As the engine winds down, tailwind may blow gasses forward and enter the manifold making a not very nice smell in cabin?
A lot of these valves are pneumatically operated; not knowing anything about the Lear, if you shut down the engine, you may possibly run the risk of not being able to shut them until you next get bleed air from a running engine.
Both of the above (as you can probably tell) are guesses.