This actually has a lot to do with your previous question about Agnes and Amalric. To summarize here, they married in 1157, and had two children, Sibylla (1160) and Baldwin (1161), but were forced to annul their marriage when Amalric unexpectedly became king on the death of his brother Baldwin III in 1163. Amalric then married the Byzantine princess Maria Komnene, and had another daughter, Isabella (1172). Agnes married twice, first Hugh of Ibelin, and then Reginald of Sidon.

Amalric died in 1174, and was succeeded by his son, now Baldwin IV, who was only 13 years old. By this point it was already suspected that he was a leper, and although he ended up living longer and being quite a bit stronger than expected, it was clear that he would never be able to have children, so Sibylla’s future marriage and children were an extremely important question for the nobles of the kingdom. While Baldwin IV was still underage (until he was 15), the kingdom was governed by one of Amalric’s cousins, Raymond III, the Count of Tripoli. Raymond arranged for Sibylla to marry the Italian crusader William of Montferrat in 1176. William died soon afterwards, leaving Sibylla a 17-year-old widow, pregnant with her son, also named Baldwin, who was born in 1177.

The other important event of that year is that Amalric’s widow Maria Komnene married Balian of Ibelin. This is important for later, but there were clearly different factions developing in the kingdom - in the past, older historians like Steven Runciman often described this as a conflict between the “native” nobility of the kingdom (Raymond III, the Ibelin family, etc) and “newcomers” who had recently arrived on pilgrimage/crusade from Europe (the Montferrats, the Lusignans, haven’t mentioned him yet but also Raynald of Chatillon). More recent historians (e.g. Bernard Hamilton, Peter Edbury) have instead depicted this as a struggle between the two sides of Baldwin IV’s family, i.e. his father’s relatives and their allies, and his mother’s family and allies.

When Baldwin IV began to rule on his own, he brought his mother Agnes and her family back to the royal court, something that the nobles of the kingdom had been trying to avoid when they forced the annulment back in 1163. Baldwin appointed his uncle, Agnes’ brother Joscelin, as seneschal, a high-ranking position. In 1180 they arranged a new marriage for Sibylla, to a French crusader, Guy of Lusignan. It’s not really clear what happened but apparently Raymond III tried to get Sibylla to marry Baldwin of Ibelin instead, and he may have even attempted a coup, but whatever happened, Raymond was outmanoeuvred by Baldwin IV/Agnes/Joscelin, and Sibylla married Guy. Guy quickly became quite powerful, sometimes acting as regent for Baldwin IV when Baldwin’s leprosy kept him bedridden.

In 1183 there was another significant marriage: Amalric and Maria Komnene’s daughter Isabella married Humphrey IV of Toron. This meant that Isabella was no longer living with Maria and Balian, and now she was part of the household of Humphrey’s family - Humphrey’s stepfather was Raynald of Chatillon.

Raynald was infamous for acting quasi-independently out on the eastern frontier of the kingdom, attacking Muslim caravans and pilgrims. Guy didn’t stop him, so both of them fell out of Baldwin IV’s favour. Baldwin arranged for his nephew, Sibylla’s son the other Baldwin, to succeed him when he died, instead of Guy and Sibylla. And that’s exactly what happened in 1185, the eight-year-old Baldwin became Baldwin V. He died too though, not long afterwards in 1186 - there were rumours that he was poisoned (and if you’re watching the director’s cut of Kingdom of Heaven it’s implied that he had leprosy too and it was Sibylla who poisoned him), but apparently he just got sick and died, which was not uncommon for medieval children.

So what was supposed to happen next? Sibylla was the next closest relative but Baldwin IV clearly hadn’t wanted Guy to become king. The next closest relative after Sibylla was their half-sister Isabella, whose claim was supported by Raymond III and the Ibelins. The next part of the story is pretty bizarre - in Jerusalem, supposedly everyone agreed to let Sibylla become queen, as long as her marriage to Guy was annulled (like Amalric and Agnes’ had been). She accepted this, as long as she could choose her own husband. As soon as she was crowned, she declared Guy was her new husband and her co-ruler.

Meanwhile, Raymond III, the Ibelins, Isabella, and Humphrey were still asserting Isabella’s claim, not in Jerusalem but in Nablus. This could have led to civil war, but then Humphrey suddenly switched his support to Sibylla and Guy instead.

It’s all a bit preposterous. Since the Battle of Hattin occurred the next year in 1187 and the kingdom totally fell apart, leading to the Third Crusade and a lot more craziness, and most of the accounts of these events were written long afterwards in the thirteenth century, based on rumours and family legends…I’m sure “what actually happened” was probably a bit different.

Finally, to get to your actual question, we don’t actually know where Reginald of Sidon was during all this. Was he in Jerusalem or in Nablus? Did he support one side or the other, or was he neutral? I should also note that Agnes had died by this point, we’re not exactly sure when but apparently sometime between 1184 and 1186. Reginald ended up marrying Helvis, the daughter of Maria Komnene and Balian of Ibelin. But when did that happen? We don’t know that either! Were they already married in 1186? Maybe, and if so, then that would probably explain why he supported the Raymond/Ibelin side rather than Sibylla and Guy.

It’s also possible that he simply didn’t like Guy, for the same reasons that Baldwin IV didn’t, because Guy was too ambitious, too impatient, a poor strategist and a poor leader. While Guy is probably not solely to blame for the defeat at Hattin in 1187, it was certainly perceived as being his fault. Maybe people like Raymond and Reginald could see what was going to happen.

So, hopefully this isn’t a bewildering amount of names and dates. It’s confusing for everyone, including me and I’m a professional crusadesologist. (When I was a student, going over all this in my head was a good way to fall asleep.)

But the very short answer is that in 1186, Agnes was probably already dead, so Reginald no longer had a family connection to Sibylla; Reginald may have already married Helvis of Ibelin, and would therefore probably have been allied with the Ibelin faction; and he may have simply recognized that Guy would be a terrible king. But since we don’t know where he was in 1186 or who he supported, the real answer is we just have no idea.

Sources:

Peter W. Edbury, "Propaganda and faction in the Kingdom of Jerusalem: the background to Hattin”, in Crusaders and Muslims in Twelfth-Century Syria, ed. Maya Shatzmiller (Brill, 1993)

Bernard Hamilton, “The titular nobility of the Latin East: the case of Agnes of Courtenay”, in Crusade and Settlement, ed. Peter W. Edbury (University College Cardiff Press, 1985)

Hamilton, Bernard. "Women in the crusader states: the queens of Jerusalem (1100-1190)”, in Studies in Church History Subsidia 1: Medieval Women, ed. Derek Baker (1978)

R.C. Smail, “The predicaments of Guy of Lusignan, 1183–1187”, in Outremer: Studies in the History of the Crusading Kingdom of Jerusalem, ed. B.Z. Kedar, H.E. Mayer, R.C. Smail (Yad Izhak Ben-Zvi Institute, 1982)

Bernard Hamilton, The Leper King and His Heirs (Cambridge University Press, 2000)