A drop tank for the Bf 109,which was entirely possible in 1940,would have dramatically incresed the endurance of the aircraft. Range was not really an issue with airfields 20 odd miles from the English south coast, across the Channel in northern France.
This was a situation not envisaged by pre-war RAF planners who had not anticipated the arrival of bombers,escorted by single engine fighters,over southern England.
There is absolutely no need for the sort of fuel loads carried by later war allied aircraft carrying out deep penetration raids into Germany across hundreds of miles of the North Sea and continental Europe. Such loads,unlike a drop tank,were,and remained,impossible for the Bf 109.
Fighter Command wasn't interested in standing patrols. Both its principal fighters were short range interceptors developed not in isolation but as part of a system. Dowding considered standing patrols to be inefficient use of his limited force,a pointless way of using up engine hours and tiring out his aircrew. The whole point of developing a well coordinated air defence system was to avoid exactly that sort of thing.
The adoption of standing patrols is not to be confused with the sort of small reconnaissance flights used to distinguish between the different types of raids Airframes mentioned near the start of the thread.
Cheers
Steve