In case you are still wondering I've just read through Steinhoff's journal while with JG 77 in Sicily. Poorly translated in regards to unit types, but hey that's what cross checking is for. The Luftwaffe used landing grounds as temporary assignment fields for operational reasons such as staging aircraft for intercept patrols. By the time of the invasion started in Sicily they used them to hop around every day to avoid bombardment and massive aircraft loss while they retreated (still unavoidable!). They managed to cram two fighter groups onto one at one point.
Also picked this up from the website you linked, perhaps you read it.
Quote:
Landeplatz: landing field or landing ground (minor – limited services or no
services).
So I would be thinking grass strip with nothing on it but a few AA and an "HQ" tent. I would say 2 steps if we had true 1:1 Fighter Group sizes, but 1 step would be the max.
I'll see if I can find some locations, most descriptions gave vague compass directions from a major field or town. Mt. Erice seems to be a main focal point.