Has the neuro-linguistic programming visual model been scientifically tested? According to the NLP visual model, fast flickers of the eyes in left/right and the 4 diagonal directions map to simple cues related to how a person is thinking. Thease are "visual constructed", "visual remembered", "auditory constructed", "auditory remembered", "kinesthetic" and "internal dialogue".

The same directions are generally mapped to the same cues but not always, additionally the left/right is reversed in the left handed. There are other cues such as in the neck that indicate further when combined with cirtain eye cues, not to be confused with observation of muscle twitches when thinking about an associated action that also occurs in NLP.
Sequences of these combine to indicate thought processes.


Have these propositions about these cues been scientifically tested?
If so, what are the results?
Yes, there's been scientific tests. No, they did not support the propositions. However, some supporters of the propositions argue that existing empirical tests have methodological problems.

There's a discussion of scientific evaluation for NLP on wikipedia that cites several review articles.

Quoting the Heap (1988) review as quoted in Wikipedia:


  Michael Heap (1988) conducted a systematic review of the research
  literature on NLP and found that it was lacking in evidence.
  
  The present author is satisfied that the assertions of NLP writers
  concerning the representational systems have been objectively and
  fairly investigated and found to be lacking. These assertions are
  stated in unequivocal terms by the originators of NLP and it is clear
  from their writings that phenomena such as representational systems,
  predicate preferences and eye-movement patterns are claimed to be
  potent psychological processes, easily and convincingly demonstrable
  on training courses by tutors and trainees following simple
  instructions, and, indeed, in interactions in everyday life. Adding,
  
  Therefore, in view of the absence of any objective evidence provided
  by the original proponents of the PRS hypothesis, and the failure of
  subsequent empirical investigations to adequately support it, it may
  well be appropriate now to conclude that there is not, and never has
  been, any substance to the conjecture that people represent their
  world internally in a preferred mode which may be inferred from their
  choice of predicates and from their eye movements. […] These
  conclusions, and the failure of investigators to convincingly
  demonstrate the alleged benefits of predicate matching, seriously
  question the role of such a procedure in counselling.


References:


Heap, M. (1988). Neuro-linguistic programming, In M. Heap (Ed.) Hypnosis: Current Clinical, Experimental and Forensic Practices. London: Croom Helm. FREE PDF