I have to disagree, very slightly and respectfully, with Flitch. Mr. Lees's comment on the introduction of the belaying pin is pretty sketchy - and, as Flitch correctly points out, relates strictly to English warships. And the coverage of his book starts after the period we've been discussing. To assert positively that a Spanish galleon of 1588 would have no belaying pins at all is to assert too much. It's certainly possible that such a ship would have no belaying pins, but the evidence isn't firm enough to support such an assertion.
The equally knowledgable (and somewhat more recent) book by Brian Lavery, Anatomy of the Ship: The Colonial Merchantman Susan Constant, 1605, has this to say (p. 37): "Racks of belaying pins were not known as such, but both Mainwaring [English, 1623] and Boteler [French, 1630s] mention 'ranges', which were rather like small versions of the main bitts, with two verticals and a horizontal piece. Each horiontal had 'divers wooden pins through it, to belay ropes unto' (Mainwaring p. 207). These were the forerunners of the belaying pin, though it cannot be assumed that they had the characteristic shape. There were only two of these ranges, one aft of the foremast and one on the beakhead, 'before the woldings of the bowsprit.' Mainwaring mentions various ropes which are fitted to these ranges, kincluding most of those of the spritsail; in general, this has been followed [in Mr. Lavery's reconstruction of the Susan Constant]. The vertical of the foremast range also serves as the knighthead for the halyard of the foreyard. Each range has eight pins."
Both those sources are a little late for our present purposes - and neither of them is Spanish. But, as I noted in my first post in this thread, to my knowledge nobody has yet found a contemporary Spanish source that would answer the question definitively.
R.C. Anderson, whom we've mentioned earlier in this thread, says something generally similar: that belaying pins (though they may or may not have been referred to by that name) were in use in the seventeenth century, but nowhere near as frequently as during later periods. (He adds the comment [p. 79] that "in a general way they did the lightest work.)
I mentioned Mr. Kirsch's fine book in my first post in this thread; I think it's probably the best place to start on a project like this. The Conway's History of the Ship volume that I mentioned earlier does express some reservations about it, though, describing it (p. 178) as a "modern attempt to understand the galleon as a European-wide ship type. Nicely illustrated, knowlegeable about England, and cites souces from other areas in northern Europe. Demonstrates little knowledge about maritime history in southern Europe, however, which detracts from the general value of the book." The tone of that comment rubs me slightly the wrong way, but it does suggest that a great deal of research remains to be done regarding Spanish galleons.
Bottom line: if I encountered a model of a Spanish vessel from 1588 that didn't have any belaying pins, I wouldn't criticize it on those grounds. I also wouldn't criticize such a model if it had a few belaying pins in the crosspieces of the bitts at the feet of the masts, and on the beakhead. But if it had long rows of belaying pins in pinrails inside the bulwarks, or on racks secured inside the shrouds, I'd think it probably was anachronistic.