Consider the reasons for the campaigns against the various Vichy colonies.
Dakar was undertaken because of reports that the Vichy government had offered the Germans its’ use as a U-boat base, directly threatening the convoy routes from the South Atlantic. The naval forces involved were diverted from their duties in the North Atlantic for what had been expected to be a few days diversion from the usual operations and was essentially a continuation of the war against Germany.
Syria was invaded because German aircraft had landed and refuelled there on their way to Iraq. It was undertaken with whatever could be scraped together in Palestine and with forces just back from Crete.
Madagascar was invaded because messages between Berlin and Tokyo had been decoded with the Germans offering the ports of Madagascar for use by Japanese submarines. The forces used were on their way to India, Ceylon and Burma and were diverted for another ‘temporary’ operation. Just how close Japan was to using Madagascar as a base is shown by the fact that a British warship was torpedoed at anchor by a Japanese mini-sub in the port of Antisiranana shortly after the town was captured by British forces.
Each campaign was a direct reaction to Axis actions or to prevent imminent Axis actions.
Other Vichy colonies were ignored, regardless of their strategic importance and however lightly they may be defended, Djibouti and French Indochina for instance, because the British simply didn’t have the forces to spare for discretionary actions; it was the absolutely critical operations and nothing else.
In the Pacific the British were walking a fine line; they wanted to support the Nationalist Chinese because they saw that as a way of limiting the Japanese, but they didn’t want their support to be so blatant that it provoked a Japanese attack.
Likewise they were willing to support American actions and American proposed embargoes but were absolutely terrified that the American embargoes would result in provoking a Japanese attack on the European colonies of South East Asia that the American’s, having provoked the attack, would take not action to defend.
The British had next to no air and sea forces in the Pacific and precious little land forces, and they were unwilling to divert forces away from the war in Europe and the Mediterranean to prevent a war in the Pacific that may not even eventuate.
It also needs to be remembered that the Japanese had an intelligence network thoroughly covering all of South East Asia; a British Fleet isn’t going to sail into the South China Sea without them being aware of it.