Mad. Truly, certifiably, quantifiably mad.
Of course, the Master had always been insane to a degree, but this was more. Before this, even within this lifespan, he'd been in control, if not entirely responsible for his actions, or rather the thoughts behind them. Now, any semblance of sanity, of calm, of control, was lost to the noise, the vibration of a double heartbeat pounding away. One-two-three-four, one-two-three-four.
It was a sound that the Doctor was never aware of. In the same way that your average human never paid attention to the wet thub-thub, thub-thub of their own hearts, why should he catalogue his own heart rate unless something were wrong with it? And, if this ubiquitous tapping and drumming and clapping and thrumming was a true representation of the Master's heartbeat, there was certainly nothing wrong there.
Consequently, logically, he thought the Master was simply paranoid. Over-conscious of his own mortality after going through more life cycles than was natural. He thought the sound in his old adversary's head, only ever mentioned after his resurrection during the Time War, was nothing more than a little more of that madness, that paranoia seeping through the cracks. A more lethal Stalin.
But in that moment, the moment in the middle of a London wasteland, in darkness, in pain, in desperation, in the moment when the Master had reached out for the Doctor, had cradled his face, had pushed his fingers to his temples and rested their weary foreheads together, in that most intimate of moments, the sharing of minds, of everything that was them, the Doctor realised.
It was real.
His old enemy, and even older friend, was not merely mad. He was suffering from his madness. The sound which plagued him did not merely whisper, nor shout, nor scream. No, it penetrated every synapse, every neuron and shook them forcibly. That sound said listen in a way that made it impossible not to hear. To hear, to listen, to focus. Every nanosecond of every heartbeat. Always there. ONE-TWO-THREE-FOUR, ONE-TWO-THREE-FOUR.
The Doctor had flung himself backwards, unable to stand the onslaught, and he had seen that desperation in the Master's eyes. And when the Master had realised that the Doctor had heard it, it had been the most heartbreaking thing.
"It's real!" he had cried, shouting out to the stars.
For all his centuries, for all his genius, in that instant the Master was nothing more or less than an insecure child who needed to be reassured. He was pure relief, exuding only the one emotion in the way that only a child can.
It was real.