There are a lot of qualifications to your question that make a lot of the answers slightly miss the premises. I would argue that there is a systematic reason for the discrepance. If a group of secessionists wants to leave one country to join another, this by definition adds a third party to the conflict. It can never be a fight between the country holding the territory and the people wanting to leave, but must always include a positioning of the country they want to join. In fact, most of the time the "receiving" country will take an active part. And the military might of the two countries involved will be much more of a deciding factor than the secessionist fighters themselves could hope to be.
In that sense, here is another example that does not quite fit:
In 1918, both Azerbaijan and Armenia declared independence from the Russian Empire. Both countries claimed the Nagorno-Karabakh region for themselves. In August 1919 both countries signed a "provisonal treaty" that accepted Aseri sovereignity of the region under the rules of a partial autonomy. After several more rounds of conflict, in 1923 Nagorno-Karabakh was finally declared an Autonomous Oblast of the Azerbaijan Soviet Socialist Republic.
After 1985, the Armenians living in the region started to rebel again against the Azerbaijan rule. Until the end of the Soviet Union, this remained a more or less small scale uprising, but in 1992 escalated to a war between the two countries.
In 1989 the Armenian Supreme Soviet had declared Nagorno-Karabakh to be a part of Armenia. In 1991 Nagorno-Karabakh declared itself independent. In the years of war 1992-94, it were the Azerbaijan and Armenian armies, with the help of mercenaries on both sides, that actually fought. Since the truce of 1994 the Republic of Artsakh maintains it is an independent country, despite its ability to rule being always dependent on the presence of Armenian forces and assistance from the Armenian government. Since the 2020 war, when Artsakh lost one third of its territory, Russian peacekeeping forces (yes, in this case I think they can be called such) are another part of the equation.
So, was there ever a true movement of the people to join Armenia, or was it the Armenian government hiding their annexation intent behind so-called freedom fighters? Was the Nagorno-Karabakh independence ever a real aim, or only a disguise? Was it, in any sense of the word, ever part of Armenia? The answers obviously depend on which side you ask.