Written material on this topic includes the following
"Son of Sinbad" by Alan Villiers, Scribners 1940.
"Sons of Sinbad The Photographs" British National Maritime Museum, 2006, ISBN 10:0 94806575 3 and 13:978 0 948065 75 0
"The Dhow" by C. W. Hawkins, Nautical Publishing Co. Ltd. 1977 ISBN 0 245 52655.2. This has a good description of wearing.
"Eighteenth Century Rigs & Rigging, by K. H. Marquardt, Phoenix Publications Inc. 1986 ISBN 1-881093 00 X at pp.160-162.
"The Sinbad Voyage" by Tim Severin, G. P. Putnal & sons 1982 ISBN 0-399-12757-7 SEE PAGES 178 ET SEQ.
"tHE sHIPS OF cHRISTOPHER cOLUMBUS BY x. pASTOR, nAVAL iNSTITUTE pRESS, isbn 1-55750-755-4. This shows the two smaller ships but does not clarify how the sails were handled.
"Spritsails and Lugsails" by John Leather, Granada Publishing 1979 ISBN 0 229 11517 9. Says the dipping lud sail had only one shroud which was shifted when the boat tacked.
"a sCRATCH mODELER'S lOG" by A. R. Lansir, a Moonraker Pub. 1984, ISBN 0-8168-0014-6
"Historic Ship Models The Musee de la Marine Collection", J. Boudroit, Pier Books, 2004 ISBN 0-9755772-2-0
The Lateen Mizzen in Europe by Peter Hodges pp.39-47 in No 24 "Model Shipwright" June 1978, Conway Maritime Press London. Discusses the different ways the northern and southern ships handled the lateen sails.
The net result is that the sail and yard can be to windward or to leeward and never be changed when the ship tacks (or wears). This appears to have been the practice in the Meditteranean, but in the Dhows of Arabia they usually wore and hoisted the yard vertical and manhandled the butt around the mast forward of same. The shrouds were cast off on the lee side so they did not interfere with the sail. However, in an emergency the ship could be tacked so that the sails were aback after the tack. But another type of ship called a Thoni had a gaff mizzen and lateen sails on the main and fore masts and did NOT shift the yards when she tacked, thus one was always aback.
Finally, eventually, in Europe the sail was split and laced to the mast. On experimental ships the bare forward part of the mizzen lateen yard had a lug or jib like sail attached to the part of the yard forward of the mast.
Thats all I know!!