It's a tricky one because at least one of the 'mechanics' civs - Brazil - has been an 'in-demand' civ as well. In fact Assyria is probably the least popular of the five civs revealed so far. Even when we have the full list it's unlikely we'll be able to distinguish which are the 'mechanics' civs (which we're told make up two thirds of the expansion) and which the 'popular' civs. Assyria's theme-effect is an odd fit for the Library, and appears to be a stretch to give them relevance to the new mechanics. That suggests to me they were included mainly on fan pressure and only then tied into the expansion. They also have no late-game relevance, and I'm pretty sure it was mentioned that the two-thirds Beach referred to are specifically civs that play with the late game (the example was Brazil as a civ devoted to cultural victory, if I recall correctly; significantly, not Brazil as a civ devoted to the tourism mechanic).
Conversely, a civ may not do anything mechanically new in the sense that it doesn't make use of a new BNW resource like trade routes or tourism, but it may be a mechanical civ if it has an ability that wouldn't have been possible in G&K for balance reasons and is only 'unlocked' by a change to - e.g. - cultural victory, and one which gives it advantages in combination with new mechanics. You couldn't make Poland in its BNW form when cultural victory revolved around social policies, and the civ has an advantage when it comes to unlocking ideologies even though it doesn't specifically say in the UA "Gain bonus X when selecting ideologies". Poland was a definite fan favourite, but it segues much better with BNW mechanically than Assyria, and much better with the expansion's late-game focus than Portugal. Poland is almost certainly one of the "mechanics" civs.
If the third 'fan favourite' civ has yet to be revealed, it may be the presumed Native American civ, which it would seem is not a natural fit for the late game any more than Assyria. Of course there's still no certainty there's any such civ. The Pueblo were shown as an example of a civ that was excluded for an interesting reason; nowhere was it implied that they had originally settled on 9 civs, of which Pueblo was the only one that was ditched. It could well be that numerous civs we don't know about were also floated and eventually dropped, not to be replaced by another civ from that region.
Of course it's possible than both Assyria and Portugal are considered 'mechanics' civs after all despite their limited relevance to the late game, in which case we still have two 'fan favourite' civs left to reveal.