All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The reported religious texts in this regard provide in a general sense that wearing gold is absolutely forbidden for men, whether the item is purely made of gold or only a small part of it is made of gold.
However, some scholars held that it is allowable for men to wear an item if only a small part of it is made of gold. Ibn Taymiyyah wrote, “There are opinions reported from Imaam Ahmad regarding the wearing of a small amount of gold (in Chapter of Clothing); one of them is that the religious concession deeming it allowable to wear an item when a small part of it is made of gold is general – without restrictions. This opinion relies on the Hadeeth narrated by Mu‘aawiyah that gold is forbidden (for men) except if it is a small part (of something else). Perhaps this is the strongest opinion in this regard; it was adopted by Abu Bakr. The second opinion is that the religious concession is limited to gold-plated weapons. The third opinion is that the concession is limited to gold-plated swords in particular. Another opinion suggests that the wearing of gold-plated items is strictly forbidden (for men) in all cases based on the Hadeeth reported on the authority of Asmaa’ that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Gold is impermissible, not even an amount as small as the eye of a locust.” However, this Hadeeth may be understood to refer to individual items made of gold, not to gold added to items made of another substance. There is no doubt that the wearing of individual items purely made of gold is forbidden according to the four main Imaams.” [Majmoo’ Al-Fataawa]
Based on that opinion, if the gold in that watch is only a very small amount, then there is no harm in wearing it, Allaah willing. However, it is more prudent to avoid wearing gold altogether to be on the safe side.
Allaah knows best.