This is a very common problem with the UK supra`s, they don’t have a relay between the ignition switch and starter, just one thin wire straight to the starter solenoid, the
wire is too thin for the amount of current drawn so it will get hot and gradually corrode with age causing its resistance to increase over the years. Many UK owners fit a relay, which solves the problem. The other thing to look at is the solenoid contactors in the starter motor they often wear on one side and are easy replaced. Not sure if this will help but I bought mine from this company
http://www.lsuk.co.uk which was the Lucas Co. Manufactured by CARGO part No 131831 contact kit, they only cost a few cents.