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The wiki article on the subject might need some editing then. Is the seconds of hover analogy even close?
It is close - in unrealistic theory. If you would have a massless engine in a massless rocket, but with massive propellant, the pseudo-specific impulse measured in seconds would be the time in which this massless rocket could hover by its own propellant mass in Earth surface gravity.
(All assumptions to make this work underlined)
As you can see, this number doesn't really help you anywhere when you need to do calculations with real rockets. For that, you need the number in a proper unit of specific impulse.