Correct on the Dogra not exercising any real control over GB but inaccurate on a few other accounts.
After the first Anglo-Sikh war in 1846, GB along with Kashmir was taken from the Sikh Empire by the British and sold to Gulab Singh of the Dogras. While Gulab Singh was able to establish his writ in the Kashmir valley relatively quickly, it took him till 1870 to establish any semblance of authority over Gilgit. Even then, it was at best tenuous with local monarchs exercising actual control on ground.
By 1885 the region of GB was effectively under control of the British Raj with on paper authority with the Jammu and Kashmir state and the on ground rulership with the locals. According to G. T. Vinge the region was practically independent of the British. The British were able to solicit local support through diplomacy with the local rulers. This continued until 1935 when the region was officially leased to the British by the Dogras for a total of 60 years.
In June 1947, since the independence of the region was evident, the British officially relinquished control of GB and returned it back to official Dogra rule. The Dogras then sent Ghansara Singh to establish their control as the governor of the region. In the meanwhile the Dogra plans to not join Pakistan were becoming more obvious and so the idea of liberating GB began taking root. This was further expounded by the fact that the people of GB had never accepted their forced union with Jammu and Kashmir, due to their historical differences, and were not willing to join India against their wishes under a decision made by a ruler and a state they had never accepted. So, the uprising began. Major William Brown, the then British CO of Gilgit Scouts, supported the uprising. He was however not a British political agent sent to control GB administratively. That agent had already returned. Major Brown was only the CO of Gilgit Scouts. According to him, he did it because the people wanted to join Pakistan. Which is also evident from the timeline of the events. Ghansara Singh was taken into custody on 31st of Oct, immediately after which Major Brown requested Pakistani troops be sent to Gilgit, the Pakistani flag was then hoisted on the Gilgit Residency on the 2nd of Nov and the instrument of accession to join Pakistan had already been signed by the 18th of Nov. Don't think Major Brown was in it for his or the British administrative control.
You and what foreign funded and backed insurgency?
Read his book. He supported the Gilgit Scouts in their liberation only after it was obvious to him that a coup was on its way. For a while he was afraid that the Gilgit Scouts were working against him as well, he even suspected his cook of conspiring against him. The instigators of the effort were these five gentlemen.