Despite his appearance and the reassurance of Donna and the Doctor she'd left in the TARDIS, Rose couldn't help but doubt the man with one heart. She trusted him enough to give him residence in the Tyler estate with the rest of her family, but still she feared his authenticity. He acted like the Doctor, he refused to give a name other than, but somewhere out there, she knew, was a lonely Time Lord. They couldn't possibly be the same.
Rose subtly tested his knowledge of their journeys in conversation, but he passed these inquiries to her satisfaction, and when he continued to assuage her fears, she was in an even more difficult position from which to doubt when he picked up on her tests and the familiar hurt look crossed his face.
She watched intently for all his habits such as rubbing the back of his neck and straightening his tie in embarrassment when her mother asked what had happened to half the chocolate cake. She took special notice at how, when he thought no one was looking, he stuck his fingers in the jam and licked them clean in ecstasy. She observed his tireless enthusiasm for the little things at any hour of the day, like little shops in the museum when Pete had insisted they visit. Or his overexcited fondness for quirky things unique to the human race, like motion-detecting lights in the yard or the fascinating locksmith tools used when they had gotten the keys locked in the car on vacation to Wales. And secretly she delighted in the familiarity of his comparing random objects or events to those of alien worlds, like the over-stuffed jewelry shop being akin to the planet Midnight. Minus the Xtonic sun, of course, he'd mentioned, eyeing the lighting somewhat suspiciously.
Her face broke into a grin when, as they found themselves locked out of the house, he used something that looked an awful lot like a sonic screwdriver to let them in. "Parting gift," he'd explained vaguely, and when asked why he hadn't used it in Wales, she smiled when he said, "Well that would have taken the fun out of everything."
Doubts became foggier when she found the Doctor in her room in the middle of the night, kneeling next to the bed and sleeping gently, as though he'd been watching over her. She recalled times when, after particularly harrowing adventures, she would find him in the same way in her room on the TARDIS.
True, he had no time-traveling blue police box, and the fastest way he could travel was by plane like everyone else, but he still had his uncanny ability to upset people, although he'd gotten a little more sensitive on account of being half-human. Though try telling that to the president of Russia when the Doctor had remarked casually on some aspect or another and gotten them chased out of the Kremlin. And promptly kicked out of the country, cutting vacation a tad short.
But if she'd had any room for dubious thoughts, the day she'd asked for help with her computer erased them. As he knelt by her desk and fiddled with wires, he'd pulled out his glasses, inspecting everything, twitching a few things, and then standing and grinning in satisfaction. Countless times that he'd whipped them out of his pocket popped into her mind; all those times when he was in full "alien-sleuth" mode and ready to save worlds. In the end, it was the glasses that Rose knew he didn't need. It was the glasses that he believed made him look clever. In the end, all it took were those glasses and she knew she was with her Doctor.