You wrote:
For the purposes of this question I would assume that it's fairly common knowledge in psychology that people touch nose or cover the mouth when saying something part of them does not believe to be true.
Avoid make assumptions like this. This is not common knowledge, and in fact it is not even true.
Vrij et al. (2010) discuss the literature on non-verbal lie detection and conclude:
The meta-analyses that have been published to date
have made clear that there are no nonverbal and verbal cues
uniquely related to deceit. In other words, reliable cues to
deception akin to Pinocchio’s growing nose do not exist
(DePaulo et al., 2003; Masip et al., 2005; Sporer & Schwandt,
2006, 2007; Vrij, 2005)
Vrij & Granhag (2007) mentions "touching the nose" as an example of a non-verbal cue to deception found in a police interrogation manual, Gordon & Fleisher (2002). They also review 5 other police interrogation manuals which don't mention it as a cue to deception. In my brief lit search, I couldn't find any psychology papers which discuss touching the nose as a reliable cue to deception.
After a brief look at Gordon & Fleisher (2002), it is clear to me that their methods are pseudoscientific, full of ad-hoc reasoning. Judge for yourself:
There appears to be a link between deception and the nose. Perhaps it is because the nerve network for emotions, to a large extent, evolved from our neural networks involved in smelling [26]. The sense of smell was primitive man's fundamental survival mechanism. Touching or pinching the nose is a reliable gesture of disbelief [4]. The nonverbal message appears to be "it stinks' (Figure 9.17). If you are talking and the listener pinches his nose, he is nonverbally communicating that he thinks what you are saying stinks. If he is talking and pinching his nose, he thinks what he is saying stinks.
Oh, but what's that reference they cite? Surely that must shed some light on this. Diligent readers will scan to the bibliography only to find that they are citing a previous version of the same manuscript! Yes, you heard right: a recursive citation. Not exactly the most reliable source.
Vrij & Granhag (2007) suggest:
Since cues akin to Pinocchio's nose do not exist, lie detectors will fail in their task if they just look for such cues. Rather, interview techniques need to be employed, for example, to control for individual differences between individuals.
References
Gordon, N. J., & Fleisher, W. L. (2010). Effective interviewing and interrogation techniques. Academic Press.
Vrij, A., & Granhag, P.A. (2007). Interviewing to detect deception. Offenders' memories of violent crimes, 32, 279.
Vrij, A., Granhag, P. A., & Porter, S. (2010). Pitfalls and opportunities in nonverbal and verbal lie detection. Psychological Science in the Public Interest, 11(3), 89-121. PDF
