Observers in Jakarta have suggested it was that same ambition which led to his being replaced as TNI commander earlier than expected by Mr Joko last December; General Tito, on the other hand, was promoted twice by the President within a year in 2016.
While it is not certain at this stage if either general will end up in the race, it would not be surprising if both do, in this current round of elections or the next in 2024.
It is natural to see ambitious generals fancy a political career after retirement because of the reverence in which many Indonesians still hold its military men.
The coming presidential election will very likely see opposition chief Prabowo Subianto, a former three-star army general, going for Round 2 against Mr Joko, having lost to the latter in the 2014 race.
Today, a number of former generals play key roles in government. They include Cabinet ministers such as Mr Luhut Pandjaitan, Mr Wiranto (another unsuccessful presidential candidate), national intelligence chief Budi Gunawan, and senior lawmakers such as Mr Tubagus Hasanuddin.
As many as 18 retired generals have registered to contest in the June regional polls.
Among them are five – from both army and the police – who specially requested early retirement in order to do so. They are: Army Strategic Reserve Command (Kostrad) chief Edy Rahmayadi, Riau Military Resort Command chief Edy Nasution, police Mobile Brigade (Brimob) chief Murad Ismail, East Kalimantan police chief Safaruddin, and West Java police chief Anton Charliyan.
What makes them potentially heavy-hitters are the loyalty of the men in divisions previously under their command. Kostrad, for instance, has as many as 40,000 troops while Brimob, a police counter-terrorism and tactical unit, has about 35,000 officers stationed across the country.
That so many former generals are seeking public office has inevitably raised questions about the role of the security forces in Indonesia. Specifically, should Indonesians be worried about the military making a comeback despite political reforms instituted after the fall of Suharto?
During the New Order era of Suharto from 1965 to 1998, the military, then known as Angkatan Bersenjata Republik Indonesia (Abri), was a key player not just in defence and internal security but also in sociopolitical affairs.
Reforms implemented after Suharto’s ouster in 1998 saw Abri relinquishing its role as a major force in national development under the so-called “dwifungsi”, or “dual function”, mandate which granted the military power over civil and political affairs.
Gone too were the seats reserved for Abri representatives in Parliament as the country, which suffered decades of authoritarian rule, aspired to a more liberal democracy.
Abri was renamed the TNI and, on paper, restricted to an external defence role, while the police, once part of Abri, has been carved out to oversee law and order at home.
Today, TNI generals who want to enter politics can do so only after they retire, usually at 58 – a move to ensure the military’s neutrality.
Mr Evan Laksmana, a researcher at the Jakarta-based Centre for Strategic and International Studies, said there are worries over the erosion of the military’s neutrality if more retirees enter politics, especially if they openly negotiate with parties before they retire.
“Others are concerned that the retirees will promote the TNI’s interests or potentially misuse the territorial command structure for local political purposes,” he wrote in The Jakarta Post last month.
Another concern is that despite the institutional safeguards, there is little that can be done to check the informal influence of military leaders who often retain the loyalty of their troops even after retirement. This is especially the case with four-star chiefs such as Gen Gatot and Gen Tito, who command forces at a national level.
Another advantage that former military politicians share is that while “dwifungsi” is no longer an official doctrine, the military’s role in civilian matters has quietly grown in the past two to three years. Soldiers have been deployed to fight forest fires, support infrastructure projects, and distribute humanitarian aid during emergencies in remote areas.
Such activities give them a lot of clout at the grassroots and are in many ways a useful platform for ambitious officers to launch their political careers.
Despite these developments, other signs suggest that Indonesians need not fear the military coming back in a big way or the TNI becoming a political vehicle like Abri was previously.
First, research has revealed that former candidates from the military have generally not done very well in elections despite their in-built advantages.
Figures compiled by Mr Laksmana showed that of the 39 military retirees who contested in direct local elections since they were introduced in 2015, only 12 won.
And while the top job has attracted former generals, only one – Dr Susilo Bambang Yudhoyono – succeeded in becoming president, winning the elections twice – the first time in 2004 and again in 2009.
What this indicates is that to succeed in the rough and tumble of politics, many skills other than those taught in military academies are needed, including an ability to build often shifting coalitions and to appeal to a wide spectrum of supporters.
A second reason that a return to junta-style rule is not on the cards is that the TNI today is a very different institution from Abri in the Suharto era.
Besides the National Defence Act of 2002 and TNI Law of 2004, enacted to prevent the military from expanding its dominance in politics, “dwifungsi” is no longer part of the military doctrine.
Furthermore, the new TNI chief Hadi Tjahjanto, and Gen Tito have made it very clear to their men and in public that the military and police are committed to remaining neutral and to working together, instead of against each other. Professionalism, not politics, should be their goal.
These assurances augur well as Indonesia moves into national election season, with regional polls mid-year and the presidential election next April.
With months of heady rhetoric, intense horse-trading and great pressure to win at all costs, Indonesia will need more than ever for its soldiers and police to keep the peace and above the fray.
At a time when Indonesia is getting worldwide plaudits for its successful transition to democracy, the better way forward is to build on it and not succumb to populist nationalist appeals, even if segments of voters may hanker for the supposed simplicity and clarity of military rule.