Apologies for the delay in responding to your query regarding two mates who served with you in Mulheim in the 1960s
With the current Data Protection Act regulations and MOD Security rules it will be difficult to obtain details direct from any Service source.
There are two other options open to you
Firstly were you Army Apprentices? Though Carlisle and Arborfield have been closed for many years now there are still active branches of the relevant Boys Association who still meet from time to time and I believe there is an active Facebook website.
Secondly RHQ REME publishes a monthly magazine which is widely circulated to both Regular and Reserve units and Branches of the REME Association (the possible link Old Comrades) world wide. Whilst there are rules on what can be published requests such as yours do appear from time to time. It might be worth your while emailing the Editor, Katy Walton, on firstname.lastname@example.org
and establish exactly what she might consider publishing