In 1302, with the fall of a garrison of the Knights Templar on which Mediterranean island, did the Crusaders lose their last stronghold in the Holy Land?

It was the fall of Ruad to the Egyptian Mamluks on Malta, hence the title Knights of Malta.

https://en.wikipedia.org/wiki/Fall_of_Ruad

The fall of Jerusalem in 1187 meant that the Knights Templar had to leave their original role of defending the Temple, and they began a series of retreats. Acre was lost in 1291, along with Tortosa and Atlit. Their main force then based itself in Cyprus, and planned on regaining a foothold in the Holy Land. A small base was established on the island of Ruad, planning to join up with Mongol allies so that the Syrian seaport of Tortosa could be recaptured. However, the Mongols never arrived, and the Egyptian Mamluks did. Following the fall of Ruad in 1302, the Crusaders had no further land presence in the Holy Land.

The Knights Templar maintained their base in Cyprus, as well as in numerous other places around the Mediterranean. The pope of the time tried to arrange for the Knights Templar to merge with the Knights Hospitaller, also known as the Knights of Malta, but neither of the leaders of these groups was interested in the merger. When the Knights Templar were suppressed in 1312, the Hospitallers were given all their assets.

https://en.wikipedia.org/wiki/Fall_of_Ruad

I have nothing to add to the original question as posted, but surely the term "Knights of Malta" for the Knights Hospitaller wasn't used until the 16th century? At the time Pope Clement V dissolved the Knights Templar in 1312, the Knights Hospitaller were based on Rhodes, having captured it as recently as 1310. They stayed there for more than two hundred years before being kicked out by Suleiman the Magnificent.