But there was no need to worry. On this occasion back in the mid-1970s the local constabulary were on hand to deliver some good news – he was about to become a Rangers player!
Dawson was just 16 at the time and a promising Ibrox ‘S’ form signing but playing for the first team was some way from his mind. Manager Jock Wallace, though, thought otherwise and decided to add the full-back to the travelling party about to head off on a pre-season tour of Canada, New Zealand and Australia.
That meant Dawson rubbing shoulders for several weeks with many of his heroes, players who just a few years earlier he had watched lift the Cup Winners’ Cup.
It was an unexpected introduction to first-team life but clearly served him well. Dawson would go on to spend the next 12 years as a Rangers player, making more than 300 appearances, becoming club captain and picking up six winner’s medals.
For a boyhood Bluenose it was a dream come true – even if he needed police approval to get things going.
He explained: “It seems a long time ago now, but that tour was effectively the start of my Rangers career. One minute you’re in school and a few days later you’re getting things packed up to go away with the first team to Canada, New Zealand and Australia.
“It was a really phenomenal experience, but at the start I admit I was a bit nervous and overawed. These were my heroes that I was travelling and playing with, although I’d got to know a few of them when I’d been in to train occasionally during the school holidays or playing for the Reserves.
“I didn’t actually know I was going on the tour until about two weeks before when the police came to my door. The club had to ask permission from my parents as I was going abroad so the police were sent round to ask the question. That was a bit unusual!
“But I was desperate to go. Luckily I’d been away with the Boys’ Brigade to Belgium the year before so I already had a passport.”
Captaining the club to glory in the 1981 Scottish Cup final was a particular Rangers highlight, even if he got a wee bit lost as he went to pick up the trophy!
He added: “I was surprised in a way to get the shout to be captain as there were more experienced players like Sandy still there. But I think John Greig did it with a view to the longer term. And that was a fantastic honour.
“Picking up the Scottish Cup was one of the biggest highlights of my days at Rangers without a doubt. It was my birthday recently and a few clips of those days came up on Facebook and one of them was of me lifting the cup. That brought all the memories flooding back.
“Luckily, Sandy was just behind me and was able to show me what to do after we’d won! He was telling me where to walk and what I should do when we got up there. So I was glad he was there to keep me right.”
Dawson remained with Rangers until 1987 before signing for Blackburn Rovers having been around to witness the early effects of the Graeme Souness-inspired revolution at Ibrox.
He recalled: “Graeme came in and made a lot of changes as everyone knows. I was there for the first year or so of it and played a few games alongside Terry Butcher, Graham Roberts, Chris Woods and people like that.
His exploits over a dozen years deservedly earned Dawson a place in the Rangers Hall of Fame, something that he still considers a huge honour.
“That was a really nice thing for the club to do,” he added. “It was just a phone call from Sandy who was on the committee at that time to ask what I was doing on a certain date to see if I was free to be inducted into the Hall of Fame. And luckily I was available! It was a real honour to be asked.”
His connection to Rangers did not end there, however. Dawson joined the coaching staff at Auchenhowie where he would serve for another decade working with – among others – the club’s under-14 teams.
Now 62-years-old, he reluctantly stepped away from coaching a few years ago.
He said: “I’m not really doing any coaching at all these days unless it’s cover for someone. I’ve had one hip replaced and I’m in the middle of seeing about getting the other one done so that was a sign telling me to stop!
“I loved my time there and all the other coaches were great to work with. It just got to a stage where my body was letting me know it was time to call it a day.”
Dawson, though, is still a regular at Ibrox on a matchday as he joins former teammates and other Light Blue legends in welcoming visitors to the club’s hospitality suites.
“Quite a few of the former players go around the suites on a matchday – it’s usually Iain Ferguson and myself doing it together,” he added.
“Some will come over after and chat away about their own memories of matches or looking to get a photo taken. It’s nice to be remembered!”
When he isn’t hosting tables at Ibrox, Dawson is as busy as ever these days in his role as a development manager with social enterprise Street Soccer Scotland.
He explained: “I’m involved with networking and building partnerships and I really enjoy it. I’ve been with them for almost a decade now and it’s a great place to work. And people are always keen to chat about the work we do whenever I’m at Ibrox on a matchday.”