If this is answered in the RAW, I seem to have missed it.
What happens when you cast spells in a situation where you're casting sigil can not appear?
There is a magus Petrafax, whose casting sigil is to cause all nearby stone and stonework to be limned in ghostly flames. Petrafax is about to go out to sea in a wooden boat, and shouldn't have any stones within sight range (unless you count the bottom of the ocean, which is too dark to see) when next he casts spells.
So do we have a case of Magus with no noticeable casting sigil?
a) Restrict casting sigils to spell effects. Sigils affect how the spell is cast, often more in terms of "how his magic works" than with specific effects. So, for example, in this case the Magus may draw on powers of Ethereal Stone (whatever that means...), so that all his spells would work (cosmetically) through applying it.
Affecting other things nearby is a Side Effect, not a casting sigil.
b) In cases where the sigil cannot be simply manifest, the spell would hopefully include it symbolically in some way. For the example Magus and sigil/side-effect, I would have the spell's effects form into shapes reminiscent of stones, or symbolizing stones in some way, or have mental effects somehow leave an impression that symbolizes stones in some way (perhaps something being "solid, yet ephemeral" or something). Again, though, if the sigil is seen as "the way the wizard's magic works", this should be less of a problem.
I will see if I can arrange that when the time comes.
As a backup I will say several of the sailors are superstitious and wear a necklace holding a stone with a hole. And then there is a whetstone. With some thought I may be able to find other stones or board the boat.
It seemed such a good casting sigil when first described. The backstory was the magus as a scared kid first used magic to make a looming stone bust burn like a torch, so ever since then stone gets ghostly flames when he casts.
The absence of stone shouldn't interfere with casting and the sigil becomes essentially invisible to all but magical investigation. However, as you later note, there should always be bits of stone around even on a ship. Whether as you say some sailors might wear carved stone trinkets, stones are used for balast, (I'm sure I've seen this) weights on rigging, or for sounding lines (though these were usually lead as I understand), there are stone items around that would show up a the sigil you describe quite nicely.