It's a puzzle to me. It's a totally bizarre thing to do at this point in the day. All the more so when we realise what was showing at the point where he made that turn off the A85. Let's recap.
"Major road works at A82 Ardlui. Delays possible." The straight-on route takes him directly to Edinburgh, on a decent road. Turn right and you're not only on a route that's 20 miles longer, and on the Loch Lomond section of the A82 which was quite frankly a cart track in 2010, you're facing major road works which were just the start of the project to upgrade the road.
Nowadays I could just about imagine that he could have accidentally taken the second exit instead of the first exit from the new roundabout, and then once he realised, thought he'd just go on now he was there. But the roundabout didn't exist in 2010 and that turn needs a very conscious decision. A decision like that needs a reason.
Was he so reluctant to get to Edinburgh and the inevitable confrontation with the police that he shied away from the direct route to put off even
more time? I can't see it. He had promised to go straight back to Edinburgh when he spoke to the police around five o'clock at Lochgilphead. Since then he has wasted 27 minutes between Lochgilphead and Inveraray, then another hour and 32 minutes between Inveraray and Tyndrum. So he's basically two hours behind at this point. (Although "only" an hour and a half behind the estimate he gave the police, which possibly factored in the first 27-minute delay, which may have been to drive into Lochgilphead and get some food from the Co-op.) The later he gets to Corstorphine the more suspicious it's going to look, surely. It doesn't make any sort of sense for him to take a route that's going to introduce yet another half-hour delay unless he had a positive reason for doing it.
The only thing he did on that diversion route was switch on his phone. I can't see any reason for the diversion other than the phone switch-on.
The off/on phone switching pattern over the whole day seems to me very regular and very suspicious. His answer to the police as regards that is that he was trying to spare the phone's battery, and in 2010 that's not an unreasonable response. Maybe his car didn't have a USB charging point for a phone, many cars didn't, back then. Power banks were unusual. People did genuinely try to save their phone's battery. But the first three switch points are
bang on the divergence points of the northern/southern routes. Nyadd, just before the A84 and the B8075 junction, and Inveraray just beyond/before the A83/A819 junction, both ways. Coincidence? I think not. So how to explain the fourth switch (second switch-on) on the A82 in this context?
Your first proposal, that Gilroy meant to switch the phone on at Ardlui (actually I think the switch-on happened at Inveruglas rather than Ardlui, but that's not important at the moment) to show that he was north of the A82/A83 junction and so hadn't come over the R&BT doesn't make any sense. If he had wanted to send the message that he had driven the A85 route, which he had, all he had to do was to keep driving that route, straight on through Crianlarich, and switch the phone on any time he liked. Turning down the A82
towards the R&BT and switching on the phone to reveal himself passing within only a few miles of Glen Croe (albeit just driving past) is a hell of a funny way to convey "no, I really haven't been anywhere near the R&BT".
The fact that the switch-on was north of the A82/A83 junction is a strong point
against the second proposal, the theory that he was trying to make it look as if he had indeed come across the R&BT. If that was his intention we should have seen the phone going on just as he was leaving Tarbet. But, as you say, if he made a mistake and turned the phone on prematurely, that would fit the theory. That's where the possibility (from the timings) that the switch-on actually happened at Inveruglas comes in. It would be very difficult to mistake Ardlui for Tarbet, because you can't see the loch on your left at Ardlui. There are houses in the way, then the marina, then a wood, and the roadworks (which were at the crossing of the burn) where the trees end. Here's the roadworks, a few hundred yards past Ardlui, and you still can't see the loch.
You do see the loch shortly after that, but the road doesn't run along the shore until just past Stuckindroin Farm. After that, though, there's a stretch of about three miles where the road hugs the shore before you get to Inveruglas. I'm not saying Inveruglas is easy to mistake for Tarbet either, but given the half-light, and Gilroy's inevitable physical and mental tiredness by this time, the possiblity that he saw the hydroelectric power station and a couple of houses and thought he was in Tarbet isn't entirely fanciful.
There's no particular reason he had to turn the phone on the instant he passed the relevant junction. He could have waited till Balloch, even, and still accomplished his objective (if that's what it was). He really, really should have waited till he was definitely past the A82/A83 junction before switching it on, and that junction is pretty damn obvious, given that traffic coming south on the A82 from Ardlui has to give way to traffic coming from Arrochar on the A83. But he wasn't necessarily familiar with that section of the road (although he was familiar with it south of Tarbet) and tired, stressed, half-light and so on, maybe he thought that was Tarbet. The other three phone-switches were carried out within a couple of hundred yards of the relevant road junctions. Whereas there would have been no issue in waiting a bit before switching on (or indeed switching off a bit early), his
modus operandi suggests he was going for the junctions. So, his tired and stressed brain thinks he's driving through Tarbet, he switches the phone on, and maybe doesn't realise his mistake until he actually does get to Tarbet, about three miles further on.
The trail of phone tracks is actually very clever, assuming he was doing what we think he's doing. Absolutely nothing on the way west to indicate whether he'd driven via the R&BT or Tyndrum. On the way back, nothing to indicate which way he went after Inveraray. If he'd replicated the westward routine on the way home, he'd have switched back on somewhere around Nyadd again. That would have left it entirely up in the air as to which way he'd gone, either direction. That's one hell of a search area, and he could have gone for that option. But it still leaves the Tyndrum route on the table. So, on the way back, turn south in Crianlarich, drive down the A82, and turn the phone on at Tarbet. That really turns the spotlight away from Tyndrum (and Glen Orchy) and focusses it on the R&BT.
He could have done the same thing on the way west, of course. Taken the B8075, A811 and A82 to Tarbet, switching off just before Tarbet, and making it look as if he'd turned left towards the R&BT. Maybe he hadn't thought of that at that stage. Maybe he just wanted to get directly to his chosen disposal site at that point, and save the misdirection for the way back. Maybe he thought that doing it twice would be very difficult to explain if for some reason the police did figure out that he'd gone a very peculiar route.
If the first three phone-switches happened at these precise points purely by chance, when he was only thinking about saving the battery, that would be one hell of a coincidence I think. Which means that the fourth switch was also part of the plan. The only way I can think of that it was part of the plan is that it was a mistake, but I think such a mistake is at least plausible. (If he hadn't made a mistake and had actually switched the phone on just past Tarbet, given that the police knew he'd passed through Tyndrum, it might have been more obvious what he was playing at. But as it was, the too-early switch-on muddies the water to the point where the police aren't getting it.)
So as you say, the police aren't especially curious about that detour. They did ask him why he did it, and he said that it was raining. I think the police know that was a flat-out lie.
But even if it had been raining, why on earth is rain a reason to make a 20-mile diversion from a perfectly good road that will take you straight to Edinburgh on to a bloody cart track with road works and delays flagged up, which will take you a good half hour longer? But when I raised this with Stuart Houston he didn't seem particularly curious about it.
I think the initial question from the police is too complicated and doesn't really nail it. "You were on your way home, having chosen (unusually for you) to take the road through Tyndrum. The road to Edinburgh was straight ahead of you. Why did you choose to turn right where there was a sign about roadworks and delays, to take a much poorer road that's 20 miles further than the direct road straight on?"
But basically yes. I spelled it out to Stuar Houston as clearly as I could, but he seems to be too much in love with this alleged sighting at the R&BT to contemplate the possibility that the R&BT is precisely where Gilroy was
not, that day.