Can we draw from any information to deduce the Thing's sex or gender? I believe it is not explicitly stated.
There is no canonical information about this, but it seems highly unlikely. The Thing reproduces by mere physical contact with another organism, so it has no reason to reproduce sexually. This suggests that the idea of sexes and genders is totally unnecessary and irrelevant to the Thing.
To the extent that the Thing has a gender or sex, it is not fixed, but contingent upon who or what it is pretending to be - in the 1982 film, every human who was assimilated by the Thing was male; however, we don't know if all the dogs, including whichever dogs were assimilated, were male. In the 2011 prequel, it does assimilate one woman, and this is the only time we see the Thing pretending to be a human female.
In the real world, organisms that usually reproduce asexually are themselves genderless and sexless. This is probably the case with the Thing as well.
The film's official novelisation (by Alan Dean Foster) explictly refers to the Thing throughout as an "it", with no assigned gender:
*Then the roof gave way and it dropped into their midst. Instinctively the three stunned men threw themselves away from the dark mass occupying the middle of the room. As he stumbled backward Macready heaved his Molotov and from the other side of the room Nauls did the same.*
This very closely mirrors the directions given in the film's draft script
Garry bolts for the main door. The Thing's tongue spirals from his mouth and spears him. The good two-thirds of its body follows its tongue and engulfs Garry by the door....
One of The Thing's talons, still caught in the door, sends it writhing in pain. It literally rips the door from its latchings and pounds it to the ground, trying to shake it loose. Nauls, hobbles, scrambles, out of the opening.