The HLI had 10 battalions during WW2, although at least one of these (7th Bn) became an Anti-Aircraft Regiment. Only the 1st and 2nd battalion were regular soldiers, with rest being Territorial Army (TA). The majority of the TA Battalions were based in and around Glasgow, and as far as I can see none of these had TA centres in or close to Taynuilt (whose population is under 1000). Of the TA battalions I think that the 9th (Lanarkshire) battalion is the most likely one to have recruited outside of the greater Glasgow area.
It is quite possible that once the war had started, and Glasgow was being subjected to bombing raids, at least one of the battalions which remained in the UK was moved out to the area of Taynuilt in order to train in the more rugged terrain. It is also possible that the beaches of Airds Bay were used to train for opposed beach landings such as those in Operations Torch and Overlord.
If you know when and / or where your father became a prisoner of war, that would provide the best clue as to the battalion he was in. This could have happened in France or Belgium in early 1940; in North Africa (circa 1942/3), Italy 1943-4, or possibly in Normandy in the summer of 1944 following D Day when several of the HLI battalions were involved in Operations Martlet and Epsom. If you haven't already done so, you should search on his name in the
National Archives and in FindmyPast's military collection if you have a subscription. As a prisoner of war, he will have been recorded in at least one Casualty report. This will provide his regimental number and location where he was captured. From there you can obtain his service record from either
the MOD or the
National Archives.
As Elwyn Soutter says, you should also contact the
HLI Regimental Museum - don't be put off by the museum's current name, the HLI later amalgamated with the Royal Highland Fusiliers.
See also
this history of the Regiment during WW2 on the HLI Association website
