NavList:

Uhm, ok, finding latitude should be easy, finding longitude, near impossible if no eclipse or other celestial phenomenon was available and even then not exactly GPS precision.

as to plausible plot, how about some statement like "one sails with sun ahead when it rises around wine harvest to get to XX, then finding two places with same name and one having been deserted for few centuries or so, this has been known to happen due to number of factors (war, pestilence, harbour silting, landslides...), this leading the earlier treasure hunters to wrong place...

using known rise/set azimuth of some celestial object seen from island at certain time of year it would be possible to find latitude to within fair precision, using that you should be able to get a "set" of islands that are possible.
to narrow it down perhaps adding something like seeing plume of a volcano erupting say and that it was in a given direction, should narrow it down some.
or possibly some feature of island, say temple rouin...

As to needing several books, we all know there are numerous sight reduction methods out there, anything from cylindrical sliderules (Bygrave, HR...) to tables of trig functions and their logarithms, even the N(x) table that can be written on one side of a creditcard and have space over.

As to tables in the 12th century, they already had access to tables of chords (Ptolemy), using those to do sight reduction should be possible, precision of calculations could likely be increased with interpolation, he gave chord every 30' but using interpolation 1/2 or maybe even 1/4 of that is possible without introducing too much error.
and around then sine formula for spherical trigonometry was known in islamic part of the world (and this being set in the med...)

main obstacle would be measuring celestial angles with precision...
using Kamal would work to reasonable accuracy, trouble would be knowing the measured angles, possibly "calibrating" it same way as a "bris"?
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