Does anyone give a useful account of tacit inferences? I am interested in the psychological notion of inference here, and do not in the context focus upon the logical notions of validity and soundness.
Tacit inference is the norm, not the exception. In a real sense, language is merely pointing with words, and we all have to infer referents from the inherently ambiguous symbols that others provide for us. Consider our interactions with young children: a young child will point and make a grasping gesture with a hand, and say (perhaps) "Gagrlagaaagah"; we are forced to infer its intent, and instinctively repeat the correct word when we figure it out. The child thus learns to point more accurately with words, lessening the burden of inference that falls on us.
Of course, as Chomsky would point out, we have built-in cognitive mechanisms that drive us to make inferences of this sort. It's hard to avoid doing so even when the inferences are ridiculous, self-destructive, or crazed (hence the wide, wide world of conspiracy theory and denialism). But waddayagonnado?
You contrast the 'psychological' inferences you are interested in with 'logical' inferences, but do not elaborate on what is meant by that or provide any citations. I will therefore presume you are not interested in formal deductive logic, but rather, in 'everyday' reasoning. As you stated in a comment:
I use the term "psychological" to refer to psychological processes in the mind or brain, and a subject may well tacitly infer something from something else without saying anything.
You thus seem to be interested in reasoning where the logic relied upon is not necessarily formalized, i.e., informal reasoning.
You do not elaborate on what you would consider a 'useful' account, but given that this is the type of reasoning which is studied in informal logic, I thought it might be useful to mention this as an answer.
Common observed patterns found in informal logic are analyzed and discussed as 'argumentation schemes' (Walton & Macagno, 2015).
Argumentation schemes are stereotypical patterns of reasoning (Walton, 1990) with a corresponding set of critical questions, namely defeasibility conditions. They represent patterns used in everyday conversational argumentation, and in other contexts such as legal and scientific argumentation.
Such argumentation schemes do not have to be cogent. A famous example is a 'direct ad hominem' argument (Walton, 2010),
Character Attack Premise: a is a person of bad character.
Conclusion: a's argument should not be accepted.
For example, calling somebody an 'amateur' or 'dilettante' based on which an argument is rejected, rather than attacking the argument itself. In and of itself such an argument does not have to be fallacious. Whether or not it is can be assessed by answering the following three critical questions.
How well supported by evidence is the allegation made in the character attack premise?
Is the issue of character relevant in the type of dialogue in which the argument was used?
Is the conclusion of the argument that A should be (absolutely) rejected, even if other evidence to support A has been presented, or is the conclusion merely (the relative claim) that a should be assigned a reduced weight of credibility as a supporter of A, relative to the total body of evidence available?
If one of the questions matching the scheme cannot be answered, revealing a critical gap in the argument by pinpointing a required assumption that is not justified, the original argument defaults.
Such a "required assumption that is not justified" are called implicit premises (or missing/unstated/unexpressed premises), which might be what you hint at when referring to 'tacit inferences', though your description is extremely concise so I can only assume.
One potential difference in your definition might be that a lot of the work in informal logic presumes such reasoning is externalized (verbalized or written), since these are the arguments that are analyzed. Completely unexpressed reasoning might rely on even more implicit premises and intuitions. As part of externalizing reasoning you might come to new insights and make more premises explicit. Either way, this body of work seemed relevant to add as an answer. In case this is not what you are interested in, perhaps it can inspire you to formulate a more specific question.
Walton, D., & Macagno, F. (2015). A classification system for argumentation schemes. Argument & Computation, 6(3), 219-245.
Walton, D. (2010). Formalization of the ad hominem argumentation scheme. Journal of Applied Logic, 8(1), 1-21.