"Is this a Compact hose? It doesn't look like a Lux hose."
No, that is a hose for a Eureka upright.
The fitting is designed to clip into an access port under a clipped cap in the exterior hood casing above the brushroll, on the body of the machine below the headlight. The fitting inserts down and then rotates inward, cutting off airflow from the main brushroll intake bottom plate, directing near full suction through the hose.
It was a convenient innovation over other brand's methods to attach a hose for above-the-floor cleaning - most others were awkward slide or clam,p on affairs that covered the entire width of the brushroll plate - of accomplishing this for above-the-floor cleaning. It appeared on two-tone blue Eurekas just prior to the top mounted rug height dial.
In another note:
Saran braided Eureka hoses are renowned for retaining their flexibility and air tightness long after other brands braided hoses have become leaky. Most of mine from the 50s and 60s Mobilaire hams, Rotomatics, canisters and uprights alike, are still 'thump' worthy.
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