Following the experiences of the students, it seems that this focus on making themselves 'the product' is not just a distraction, but also counter-productive. The first problem is that the proposition comes from the paradigm of lifetime employment, somewhat a reality in the 'golden age' of industrial civilisation (at least for the middle classes), but true no longer. With this, getting in was the most difficult part, and once you have managed that, there was an automatic progression through the stages, ending up in retirement. But, now, not just getting in isn't enough, you actually never get in unless you have crossed several pre-stages, small employment and projects, successfully. So, getting the expectations right, choosing interesting internships, making connections, turning up at right networks, learning things while doing work, and being consciously pushing for progress - are really important. But, all this gets obscured when one believes that it is really about writing the CV properly.
In the Conclave, I made an observation, somewhat in jest, that the only skill that seemed to matter in India is English language. This may be just an anecdotal observation, but, I shall claim, there may be a deeper truth in it. The route to employability in India is in learning the language of the business, i.e., English. This may have slightly different connotation, but holds true for other countries too: To be employable, what's most important is to pick up the language of the game (Wittgenstein will approve). This is why the 'practical' learning is so coveted by the employers, not because it teaches more but it makes the learner talk the language. So, the original question - what does 'employability' means in practise - can be answered with 'teaching the appropriate language'.
The problem is that each type of business, each organisational form, may have a distinct language. Focusing on teaching a specific language carries the risk of making the students' abilities completely redundant, without the crystal ball gazing into where they would end up. This is the mistake lots of vocational providers do: They focus almost solely on the language of the business, particularly as they are often guided by 'Sector Skills Councils'. In a society where most of the rewarding professions have been created in the last two decades, being guided by an expert with thirty years previous experience in the trade is no guarantee that that trade will actually exist or be able to absorb the student in question, thirty years hence.
So, the sustained employability of the kind I spoke about in my answer can come from only two things: Knowing the language of the business from inside but also from outside, a kind of consciousness why what is said is said. This is common sense, but does not happen, because these two things stay in two different boxes as far as education systems are concerned. Language of the trade sits in the 'vocational' category, and the thinking about the language of the trade, the so-called critical consciousness, in the realm of 'Higher Education'. And, these categories are strongly separated: The vocational teachers treat any questioning of the language of business as unnecessary philosophising, and the Higher Education teachers believe that this language of business is somewhat low stuff, worth criticising but not worth studying with any seriousness.
The problem of employability, then, is somewhat connected to how our education systems are constructed. The artificial barriers of vocational and higher education systems, created primarily for the sake of state control and funding, comes in the way of aligning what is taught with what a rapidly changing society may need. Inside the institutions, a different game is played in turn: Inside Higher Ed, a language develops to play the game of research citation and funding, and within the vocational realm, everyone rushes to conform to various ministerial agendas. The language of education, therefore, diverges from the language of work, because business enterprises, social organisations and even public sector bodies hardly speak the language that the students and their tutors have to speak inside the colleges and universities. All the additional employability courses, based on false paradigms, flawed designs and failed prescriptions, are offered as palliative measures, but do more harm than good. The only practical measure to make students 'employable' will be to challenge the paradigm of education in the first place, and start building a new conversation within the classroom.