Yeah no, it's a war. How did the Spanish Nationalists win the war when they lost the election if it's a popularity contest?
Oh, simple!
1. They had better international support.
2. They took main support in officer corps, with army divided close enough.
Both are popularity contest issues.
And yeah, they had big, big problems early; if Republicans didn't apply to terror tactics, they could won.
The issue at hand is whether the person can lead a provisional government to victory when that faction failed to execute a coup.
No. We finding instances where such persons was called by such faction (and you actually offered Kolchak, Kornilov, and Denikin, who definitly didn't won). There is a difference.
Algerian Civil War, Zeroual was the leader there, again not a geriatric figurehead.
By the way, Zeroual. Nice example actually. Not as he managed to lead his government to victory, but nice indeed.
What happened in Alger? Islamists won local elections, then Army make coup and canceled presidential elections. For two years he was out, and then, in 1992, Army deposed President, putting in his place... well, not Zeroual. Mohamed Boudiaf. 73-yeared vet of Algerian Independence War, who spent last 26 years in exile in Morocco. Why him, not some acting general? Because "he was presented as a leader exiled for too long to be tainted by the violence and corruption of Algeria's internal post-revolutionary politics", that was official version (real one, I believe, was because he wouldn't interfere into military issues). Well, half a year later Boudiaf was killed, and he was suceded by... not Zeroual again, by Ali Kafi, retired Algerian army colonel, vet of Algerian Independence War, who was 64 years old and was diplomat since 1962. It didn't helped, so in 1994 he was replaced by Zeroual, vet of Algerian Independence War, who wasn't part of clique firstly (and was retired officer since 1990; returned as Minister of Defense in 1993). Zeroual was known as negotiator, and he actually tried to negotiate; it failed, so he offered presidential elections. Opposition was against it, but elections happens, Zeroual won and ruled until 1999, when he retired as well. He was replaced by military-backed 63-yeared ex-military (you guess) vet of Algerian Independence War, ex-Minister of Foreign Affairs, who did actually nothing in the war, Abdelaziz Bouteflika, acting president of Algeria.
In 2002 civil war ended, in 2011 emergency rule ended.
I believe Boudiaf, Ali Kafi and Bouteflika fits criteria; as you can see military faction in Algeria was quite insistent to put such compromise and amicable persons (well, as amicable as was possible!) to highest posts. And yes, they won.
Ethiopian Civil War, where Mengitsu was the leader, not a figurehead.
Ok, Derg. Another nice example.
When Derg imprisonment Haile Selassie in 1974, they named Aman Mikael Andom as a leader of state and Derg chairman (with real power concentrated in Mengitsu hands). Why? Well, because he was popular in army; being popular in Derg would be another matter, so in November, after he lost "his" military, general was killed (or suicided) and replaced by Tafari Benti. Well. Let's not notice that Derg didn't abolish monarchy until 1975, so for a year "leader" of their state would be Haile Selassie. Actually Tafari was powerless nobody, but he quickly became a crystallisation center to opposition against Mengitsu, so in 1977 Mengitsu overthown him and actually gain formal title of Derg chairman. 10 years later Derg was changed into republic (where Mengitsu was a president), and in 1991 Mengitsu leaved country (so his faction actually lost Civil War).
I'd say Aman Mikael Andom and Tafari Benti would be nice examples as well, even as they wasn't old.
Central African Republic Civil War, Djotodia is the leader there.
Once again, no victory for coup faction here (as you declaring coup-turned-into-civil-war as a main criteria, you should admit it's disqualification).
First of all, no coup faction at all. Seleca was plain rebels. Same about Baron Wars - it wasn't failed coups turned into civil wars, it was plain revolts. My lovable Warlord Era isn't fit by this criteria as well. Same Austrian Civil War - no coup.
Secondly, Djotodia failed, Central African Republic Civil War continues. Well, it's complicated, but it's not like Seleca won.
And please, don't put White Movement into this mess. They couldn't define who is their leader and what actually they trying to achieve, that was kind of problem.
But yeah, as you can notice having figureheads who actually should just give legitimacy is quite popular. If von Mackensen would be a head of provisional government, it doesn't mean Beck wouldn't be a general for coup's armies. And in Wiki he would be named as one of the leaders.
If you want another example - please, look into Emperor Meiji. Restoration named "Meiji Restoration", he is listed in English Wiki for every battle of Boshin War, and he was 16-year boy who, let's put it mildly, wasn't the best military or intellectual asset. But all that happened happened in his name and with his formal leadership. Why? Because it gave Satchō Alliance legitimacy they needed.