Born in Mexico City on 5 February 1956, Rebaque came from a family with deep motorsport roots. His father, Héctor Rebaque Sr., had competed on tracks and in rallies during the 1950s and 1960s, winning a 24 Hours of Mexico Rally and driving a North American Racing Team Ferrari at the 1967 Sebring 12 Hours in a car partly sponsored by Pedro Rodriguez, a close family friend. After retiring from the cockpit, Rebaque Sr. formed Team Rebaque to further his son's career, entering the 15-year-old Hector in local races from 1971.
Rebaque Jr.'s junior career took him through sportscar racing alongside Guillermo Rojas (including a Le Mans 24 Hours debut in 1974 in a Porsche 911 Carrera RSR), Formula Atlantic with Fred Opert Racing in both Britain and North America, and Formula Two. By 1977, aged 22, he had secured a seat with Hesketh for six races. He qualified the 308E only once — for the German Grand Prix at Hockenheim — before retiring with battery failure, and failed to qualify the remaining rounds. With no team willing to give him a seat for 1978, he chose to create his own.
The operation was established in Leamington Spa on a modest budget compared to the era's major entrants. Sponsorship came from Mexican brands including brewery chain Moctezuma under their Carta Blanca label, Domecq wines, and Café de México. The team's inner circle included Rebaque's father and Manuel "Chacho" Medina, later to become a prominent Mexican motorsport commentator. Peter Reinhardt and engineer Geoff Ferris also featured among the key staff.
For 1978, Rebaque struck a deal with Team Lotus to purchase the championship-winning 1977-specification Type 78 chassis, known internally as JPS-15, fitted with a Ford Cosworth DFV. With extremely limited experience — a single Grand Prix start to his name — the results were mixed. He failed to qualify at the season opener in Argentina, qualified 22nd in Brazil only to retire through driver fatigue, and saw a succession of retirements and non-qualifications through the middle of the year.
The turnaround came at Hockenheim for the German Grand Prix. Qualifying inside the top 20 at the circuit where he had made his debut 12 months earlier, Rebaque drove steadily from 18th on the grid to cross the line in sixth place, securing one World Championship point. He followed that with a strong 18th place on the grid in Austria before results tailed off again with further non-qualifications at Monza and Watkins Glen. The team finished the year with one point to its name.
For 1979, Rebaque negotiated a second deal with Colin Chapman to run the now championship-winning Lotus 79. Mid-grid qualifying positions were achievable but often undelivered; retirements through accident and mechanical failure dominated the early rounds. His best result in the 79 came at Zandvoort — seventh place — in what would be the car's last outing for the team.
During the season, Rebaque had commissioned Penske to design and build a bespoke chassis at Penske's British base in Poole. The Rebaque HR100, shaped by Geoff Ferris with contributions from John Barnard, drew heavily on the Lotus 79's aerodynamic philosophy while incorporating sidepod elements from the Williams FW07. The finished car was displayed in the paddock at Zandvoort but was not yet race-ready. It made its competitive debut at the Italian Grand Prix at Monza, where it failed to qualify with teething problems. At Montreal, Rebaque started 22nd on the grid, moved up four places in the opening laps, but retired after 26 laps with a broken engine mount. At Watkins Glen, with the first practice session lost to rain, he again failed to qualify. Three races, one start, zero finishes.
In Rebaque's own words, the experience of running himself as both team principal and driver had proved unsustainable: "After two years we were still having lots of problems. It was complicated for me trying to drive and trying to keep the team together… Instead of having fun, and really enjoying what we were doing it was really tough." The team closed at the end of 1979.
Rebaque joined Parmalat Brabham from the 1980 British Grand Prix onwards, replacing Ricardo Zunino as teammate to Nelson Piquet. His debut in the BT49 at Brands Hatch brought seventh place. He stayed with Brabham for the full 1981 season, which proved his strongest in Formula One.
In 1981 he scored 11 championship points to finish tenth in the Drivers' Championship. His most dramatic performance came at the Argentine Grand Prix, where after qualifying sixth he ran as high as second behind Piquet before a broken rotor arm inside the distributor ended his race on lap 33, denying him a podium. He also collected fourth places at San Marino, Germany, and Zandvoort, and a fifth in Britain. The Monaco Grand Prix was a low point: unable to qualify in a congested pre-qualifying session that left Piquet on pole but eliminated several other Brabham-adjacent entrants, Rebaque missed one of the season's most prestigious events.
Brabham chose Riccardo Patrese over Rebaque for 1982. He was offered a seat at Arrows by Jackie Oliver but instead opted for North American open-wheel racing. His 1982 CART season, driving a March 82C for Forsythe Racing, included the Indianapolis 500 where he finished 13th after a pit fire on lap 151. His greatest international victory came at Road America, where he won the first CART race held at that circuit when Al Unser ran out of fuel on the final lap. A testing crash at the Milwaukee Mile a week later convinced him to step back from oval racing. His final competitive appearance was a non-championship Race of Champions at Brands Hatch in 1983, driving a Brabham, from which he retired on lap 23 with tyre and suspension problems.
After motor racing Rebaque returned to architecture and real estate development, building and later selling hotels before concentrating on apartment projects in Mexico. The HR100 — Mexico's only purpose-built Formula One car — sits mounted in the living room of his house rather than a museum, a domestic trophy for the last man to own and drive his own team in Formula One. In 2002 he served as Grand Marshal at Road America to mark the 20th anniversary of his CART win. That same victory machine, the March 82C, was later auctioned at a Mecum Indy event in 2020, with proceeds benefiting the Motorsports Hall of Fame of America.
Team Rebaque's record is modest by any conventional measure — one point from 30 entries — but the operation's historical position is not. In an era when the gentleman driver was already fading from Formula One, Rebaque pushed further than any predecessor: he ran his own team, maintained it for two full seasons, commissioned a bespoke chassis, and brought Pemex backing to Brabham when his driving career warranted a works drive. The HR100 remains the only Formula One car designed and built on behalf of a Mexican constructor.