The most obvious shared trait is their phallic aspect. A penis is part of the traditional herma (see here, for instance) and it is usually given two meanings: either a symbol of fertility, especially in the rural settings, or an apotropaic charm (or both). It also goes well with Mercury’s more sexual side, very much in tune with pleasure and joy, all of which resonates with Ingui’s phallic aspect. Additionally, there may a connection with cattle reproduction, since Mercury is also a shepherd god, though I’ve been told that He has more to do with lust and less with procreation. The distinction may be irrelevant, but Mercury’s rurality nonetheless meets with Ingui’s connection with farming: the former protects the herds while the latter increases them; and, in the end, both provide the same result – prosperity! In the form of agricultural goods, yes, but also in terms of precious metal and money. After all, the more cattle you have, the more profit you can get, a connection still valid in today’s rural world and just as true in the ancient world. Not to mention that Ingui-Frey is the son of Njord and the brother of Freya, both deities associated with material wealth.
Agriculture also has an associated element of change, of life, death and renewal, which implies the recognition of movement. Here the common ground between the two gods is less straight-forward, but it may still be there. Both acknowledge the need for change, even if for different reasons: Ingui sees the need for life to move on, to renew itself through sacrifice and death as the seasons do every year; Mercury is connected to the movement in trade and journeys, but there may also be a side of Him that supports change in things when they’ve reach the end of their usefulness and are dragging you down. This is, at least, the impression I get when reading texts by modern devotees of tricksters. Like Ingui, Mercury can tell you to let go a dead weight; like a plant, dead branches need to be trimmed so new ones can grow, healthy and vibrant.
An even less obvious common aspect would be diplomacy. As a messenger, a patron of heralds, negotiators and gifted speakers, Mercury is at home in the world of politics. He’s even at home in dirty politics, which is made of cunning, plots and tricks, but in that I reckon Him and Ingui go separate ways. Frey is much more about honesty, rule-abiding and sacrifice, if necessary. Yet the two appear to complete each other, for even good politics requires a willingness to “play the game”. I’m actually quoting Varys from Game of Thrones here: Ned Stark and John Arryn were noble and honest men, yet they refused to play the game and that led them nowhere (expect the grave). Tyrion, on the other hand, plays the game with cunning, even throws himself into battle, but without losing sight of what’s right and wrong. A good politician needs a bit of Mercury and Ingui. Still, this is not where They meet in the diplomatic field, but rather in Frey’s status as a hostage or, at the very least, the son of one. It’s a debated topic in the academic community, but the late and surviving sources for Norse mythology mention a war between the Vanir and Aesir gods, which was settled, among other things, with an exchange of hostages. There may be more than one version implied in the medieval texts, but at the very least we can say that Njord moved to Asgard to ensure peace between the two godly groups. Frey is therefore the son of a war hostage and a product of an on-going diplomatic agreement.
Finally, there’s a more obvious and definitely universal link between Ingui and Mercury: joy! Not just sexual, which has already been covered, but general, jumping and laugh-your-pants-off kind of joy. It’s uplifting and that goes straight to the core of two life-loving gods.