He's absorbed, tapping away on a laptop on whatever work it is progressive young football coaches can do via a keyboard and screen these days. Cathro, as always, is in transit. Beside the table is a cabin bag. Within a few hours he will be on plane to Valencia.
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Most 28-year-old Scotsmen currently going to Spain are on their summer holiday. Cathro is there to help steer one of its biggest football teams. Tonight he will be in the dug-out in the Ramon Sanchez Pizjuan stadium in Seville as Valencia, his team, visit on the opening weekend of the Primera Division season. Cathro, the Dundonian who never reached any level as a player, and who has never coached senior footballers in Scotland, is one of the most interesting figures in our game.
The next chapter in his story begins tonight. "I'm living out of a suitcase. The other case hasn't been opened, it's at the side of my bed in the house in Valencia. It's kinda just about working and sleeping right now. My 'social life' is about this," he pointed to the smartphone on the table. "I maybe catch up with someone for 15 minutes when I'm back and then I have to go.
"It's 'when will you be back', 'sorry, dunno'. It is difficult. It's about having the balance right but after sacrificing so much you have to keep doing it, or it will mean nothing."
Cathro wasn't taken to Valencia by coach Nuno Espirito Santo, the manager who also took him from the Scottish Football Association to Rio Ave in Portugal in 2012, to gawp around and enjoy the sights.
Cathro helping to manage Valencia seems remarkable to us, but not to him. Was there anything left of the young kid who might be overawed or daunted by the sights and sounds he'll see tonight, and in games to come against the likes of Real Madrid and Barcelona?
"He's disappeared most of the time," said Cathro of his younger self. "When I speak to people they say 'it's amazing eh'. I say 'yeah, it's alright'. I sometimes think I'm almost under-appreciating it. I've just not interpreted it like that. It's work. It's your work. I would feel more like that [maybe overawed] if I was sitting in the stand watching another game.
"Occasionally it crosses my mind, mainly in little conversations with friends. Everybody in my life, that I know, loves football. So when it falls back into a sort of non-work general chat, and they speak about it, and I'm in 'take-an-hour-off mode', I appreciate it. The game last week at Old Trafford against Louis van Gaal . . . you could talk about that in an off-day mode. It is a tremendous situation to have been in - wow! - but the reality is that it's my work. We were there to win and we didn't win, so it remains a frustration rather than a nice experience. The switch goes."
Note how he referred to that trip to Old Trafford. It wasn't "against Manchester United", it was "against Louis van Gaal". Maybe that was a slip of the tongue or maybe it was an insight into Cathro's respect for, and fascination with, coaches and coaching. The friendly ended in a 2-1 defeat but it served as a crash course in the class of opponent, and the size of stadiums, Valencia routinely face.
Cathro was an SFA performance school coach on Tayside when Nuno, the Portuguese coach he met and impressed on a Largs course, offered him the chance to be his assistant manager at Rio Ave. They finished sixth and then 11th in Portugal, reaching two cup finals last season as the club punched above its weight. When Nuno was offered the Valencia job it was natural for him to take his young Scottish assistant.
Peter Lim, the Singaporean businessman, has finally completed a takeover of the club and having finished eighth last season the expectation - the demand, in fact, from the famously passionate regulars in the Mestalla - is that Valencia return to the Champions League. In a championship with Atletico Madrid, Real Madrid and Barcelona making irresistible claims for three of the four qualification places, the opening is narrow.
As for Cathro, he is becoming less precocious. Slowly, imperceptibly, his youth is diminishing as one of his defining characteristics.
"It's starting to happen. You see the baldness," he laughs, bowing his head. "I'm getting less and less young all the time!"
There's no denying that, but if he was a player he would only be coming into his prime years. Valencia appointed him in the week that his former prodigy, Ryan Gauld - who he coached years ago in his Cathro Clinic and at Dundee United - joined Sporting Lisbon. Cathro enjoyed the coincidence. "That was a good week: young kid who wants to be footballer, slightly older kid who wants to be coach, after us working together more or less every day for a good number of years.
"When we speak to each other or we think individually about it I don't consider that we have achieved anything yet because my expectation is that we'll both do more. But I think it is reasonable to say 'that was good, we should be a little bit proud of our younger selves for all the effort we put in'."
Sevilla v Valencia, Sky Sports 5, 8pm