I can't recall seeing a specific requirement that the problem-solving method be documented, but recall that there's a general expectation that important processes should be documented, where the availability of a documented process/procedure would prevent nonconformities.
Problem solving has always been a major priority in the auto industry, so it would make sense to have a formally documented approach. In the absence of a company preference, using the Ford
8D would be a good choice. (Other formal approaches like 5 why, Kepner Tregoe, Shainin methods, etc., are all good too but 8D is readily accessible to all.) And, by the way, at the recent AIAG Quality "Summit", the OE's expressed their concern that problem solving skills are slipping, not improving.
So, my recommendation would be to document the method... perhaps just by using an 8D based form.
Brad