Daniel Ricciardo's tally nudged over the 30-lap mark in the morning session, and he bettered the best laptime managed by the troubled RB10 throughout last week's four days at the same Sakhir circuit.
"This looks significantly better than last week," said a source in the island Kingdom.
Watching the action carefully will be world champion Vettel, who will only return to the wheel of the Renault-powered car on Saturday and Sunday.
Marko admitted to Germany's Bild newspaper that the reigning quadruple title winner and German is "not amused" that Red Bull is "so far behind" with just four days of track running to go until Melbourne.
"But getting angry won't bring us anything.
"Sebastian is always informed of any developments," Austrian Marko continued, referring to the team and engine partner Renault's scrabble to end the crisis.
"Even ten million euros wouldn't simply solve the problems," Marko admitted. "Renault needs to get a grip on the engine.
"Mercedes is a big step ahead of us, as they have already been able to do long-distance testing with their new car.
"We have worries about Australia and probably beyond," he added.