According to Derbysulzers.com they did make it as far as Perth around 1966, I have seen two photographs of peaks working out of Buchanan Street.
"Peaks continued to work out of Glasgow Buchanan Street, the 12.00 Dundee - Glasgow, 18.00 return and the 16.25 to Inverness (to Perth) were favourites with D89 noted on Feb 5th & 9th on the former two and D46 on the latter on 26th. Despite their presence in the Glasgow area the EE Type 4s were rare performers on the Dundee turns, Peak failures were normally covered by Class 5s, with the 20.00 hours from Dundee being a favourite for steam substitution. Another working to bring Peaks into the area was the 14.20 Waverley - Stirling, this was normally covered by a Gateshead Peak. A stranger on the daily Auchlochan colliery turn (formerly the Coalburn branch) was D40 on March 8th"
https://www.derbysulzers.com/66.html
Jim