Is there a specific mechanism that aids in this shift or does a specific molecule or signal trigger this change of approach? Do we know which cells in different organisms adopt this approach and is this inducible by artificial means?
Inhibition of mTOR activity by dietary restriction or blocking Akt signaling leads to an increase in eIF4E-BP (4EBP) activity. 4EBP then binds to eIF4E and prevents it from binding to the cap on mRNAs, a necessary prerequisite for cap-dependent translation. This leads to an increase in free ribosomes that then are available to initiate at Internal Ribosomal Entry Sites (IRESs). Some IRES require additional factors (ITAFs) while others respond to the increase in free ribosomes. You can induce this by feeding rapamycin or starving your organism/cells. Concentrations will be cell type specific, so it's best to do a dose response study.
It nicely delineates how all sorts of stress (nutirent deficiency, induction of apoptosis, ...) can trigger cells to enhance the translation of mRNAs containing IRESs. The classical example found in many textbooks is the upregulation of expression of the transcription factor GCN4 in yeast when switching from 'rich' to 'poor' medium. Cf Fig 3 in the review indicated above.